Unsmoothing Real Estate Returns: A Regime Switching Approach Colin Lizieri, Stephen Satchell and Warapong Wonwachara Department of Land Economy / Department

Unsmoothing Real Estate Returns:A Regime Switching Approach

Colin Lizieri, Stephen Satchell and Warapong Wonwachara

Department of Land Economy / Department of EconomicsUniversity of CambridgeEuropean Real Estate Society ConferenceMilano May 2010

Not Another Paper on Smoothing? Many studies analysing impact of appraisal process on valuation-based real estate indicesStandard method assumes time-invariant process

Can we maintain this assumption?Transaction-based indices and adjustment for liquidityTail dependence and behaviour in bubbles / crashesIntuition here: may be a regime-based structureFor returns process (Lizieri et al., Brooks & Maitland-Smith)For smoothing process (Chaplin, informal model)

The Index Issue FT Returns m 2.02% s 8.58% rt,t-1 0.014IPD Returnsm 2.15% s 3.25% rt,t-1 0.813

Chart1

2.443667650218.841917038

2.72494815.2607927322

4.9526476865.616584

5.6194024086-32.0026550293

5.19769763954.0549674034

8.0297268.310058

7.261537-0.4158257

6.685861-1.0190192461

4.790126323715.8391513824

5.1729773.7536697388

4.20709753047.152185

1.28220224384.0634436607

-0.08922204-6.530186

-2.35553145416.268623

-2.1429033279-18.13032341

-2.02860856068.147772

-1.675187230115.4552135468

-0.08520085-1.2575266361

-0.0498918310.16984272

1.0617476702-5.514645

0.2975316346-0.1393856108

0.38536563525.096318

-0.81754880.4986844361

0.0514328113.169506073

0.82941474.48695

2.48747158052.6163947582

3.8283056.1890354156

7.94688211.74033

7.538446-6.432471

3.7876107693-5.54714

1.82244086274.34841

1.05068171021.5851967335

0.90526122.368151

0.43037626.381937

0.93106047.720172

0.88311564.887479

1.74748122693.473517

2.0883445741.800711

2.07552838335.992757

3.02768754964.1683225632

2.9459095.147196

3.439779525.052799

3.43418955812.3165931702

4.5285634995-1.3730785847

3.22291515.0943746567

3.742896-0.798896

2.7978746891-14.9692277908

1.703813.5682315826

2.06999516498.746055

3.63149070742.3110244274

3.609901-3.4791407585

3.90778714.09605

3.073943615-3.4921572208

2.564726-2.1302621365

2.3092830.6456831

2.045359-1.105868

1.7740278244-8.800473

1.67057728771.1919534206

1.526315093-14.55667

1.85314834127.903409481

1.88252520562.2446427345

2.8541986942-11.5977525711

2.822395-21.8640575409

2.37972235684.577512

1.9669923782-6.516522

2.63253513.5642137527

2.7760963443.8169956207

3.27403163918.995739

3.4321490.6180823445

4.80956840522.171329

4.24031972892.8292126656

4.8249244696.4608635902

2.63518238073.003842

4.39339637764.8901615143

4.3223547.847241

5.89810037614.178603

4.35247755057.783821

4.944522-1.8546527624

3.6528843.5838816166

3.6991795.97447

2.2330381872.865909338

2.08086633684.441267

-1.0184029341-1.7781077623

-8.925352-0.3495439

-3.4403786659-10.37297

-2.696162-1.4569555521

-4.885533-12.993262291

-14.50788-10.742609024

IPD Returns

FT Returns

IPD versus FT Returns 1987-2008

Figure 1 & 3

IPD ReturnsIPD ReturnsLIBORFT ReturnsGDP GrowthLIB REGFT REGGDP REGFT 1FT2AR-TARTAR-TAR

1986Q411.251.706.25-1.54-0.41-13.33-1.2LIBOR6.25FT1-13.33

1987Q12.442.4410.0018.840.506.25-1.54-0.41-13.33-1.2FT-1.54FT2-1.2

1987Q22.722.729.2515.261.106.25-1.54-0.41-13.33-1.2GDP-0.41

1987Q34.954.9510.385.622.206.25-1.54-0.41-13.33-1.2

1987Q45.625.628.94-32.000.906.25-1.54-0.41-13.33-1.2

1988Q15.205.208.694.051.706.25-1.54-0.41-13.33-1.2

1988Q28.038.039.888.310.506.25-1.54-0.41-13.33-1.2

1988Q37.267.2611.94-0.421.406.25-1.54-0.41-13.33-1.2

1988Q46.696.6913.25-1.020.706.25-1.54-0.41-13.33-1.2

1989Q14.794.7913.0615.840.406.25-1.54-0.41-13.33-1.2

1989Q25.175.1714.253.750.606.25-1.54-0.41-13.33-1.2

1989Q34.214.2114.697.150.106.25-1.54-0.41-13.33-1.2

1989Q41.281.2815.164.060.106.25-1.54-0.41-13.33-1.2

1990Q1-0.09-0.0915.25-6.530.806.25-1.54-0.41-13.33-1.2

1990Q2-2.36-2.3614.976.270.506.25-1.54-0.41-13.33-1.2

1990Q3-2.14-2.1414.97-18.13-1.206.25-1.54-0.41-13.33-1.2

1990Q4-2.03-2.0314.068.15-0.606.25-1.54-0.41-13.33-1.2

1991Q1-1.68-1.6812.4415.46-0.106.25-1.54-0.41-13.33-1.2

1991Q2-0.09-0.0911.31-1.26-0.306.25-1.54-0.41-13.33-1.2

1991Q3-0.05-0.0510.3410.17-0.406.25-1.54-0.41-13.33-1.2

1991Q41.061.0610.94-5.510.106.25-1.54-0.41-13.33-1.2

1992Q10.300.3010.81-0.140.106.25-1.54-0.41-13.33-1.2

1992Q20.390.3910.135.10-0.206.25-1.54-0.41-13.33-1.2

1992Q3-0.82-0.829.000.500.506.25-1.54-0.41-13.33-1.2

1992Q40.050.057.0013.170.606.25-1.54-0.41-13.33-1.2

1993Q10.830.835.944.490.606.25-1.54-0.41-13.33-1.2

1993Q22.492.495.972.620.506.25-1.54-0.41-13.33-1.2

1993Q33.833.836.006.190.906.25-1.54-0.41-13.33-1.2

1993Q47.957.955.3111.740.906.25-1.54-0.41-13.33-1.2

1994Q17.547.545.34-6.431.106.25-1.54-0.41-13.33-1.2

1994Q23.793.795.16-5.551.406.25-1.54-0.41-13.33-1.2

1994Q31.821.825.854.351.406.25-1.54-0.41-13.33-1.2

1994Q41.051.056.561.590.706.25-1.54-0.41-13.33-1.2

1995Q10.910.916.632.370.406.25-1.54-0.41-13.33-1.2

1995Q20.430.436.916.380.506.25-1.54-0.41-13.33-1.2

1995Q30.930.936.787.721.106.25-1.54-0.41-13.33-1.2

1995Q40.880.886.504.890.506.25-1.54-0.41-13.33-1.2

1996Q11.751.756.063.471.006.25-1.54-0.41-13.33-1.2

1996Q22.092.095.781.800.406.25-1.54-0.41-13.33-1.2

1996Q32.082.085.885.990.706.25-1.54-0.41-13.33-1.2

1996Q43.033.036.474.170.806.25-1.54-0.41-13.33-1.2

1997Q12.952.956.315.150.806.25-1.54-0.41-13.33-1.2

1997Q23.443.446.845.050.806.25-1.54-0.41-13.33-1.2

1997Q33.433.437.2512.321.006.25-1.54-0.41-13.33-1.2

1997Q44.534.537.56-1.371.206.25-1.54-0.41-13.33-1.2

1998Q13.223.227.5315.090.806.25-1.54-0.41-13.33-1.2

1998Q23.743.747.81-0.800.706.25-1.54-0.41-13.33-1.2

1998Q32.802.807.31-14.970.906.25-1.54-0.41-13.33-1.2

1998Q41.701.706.1913.571.106.25-1.54-0.41-13.33-1.2

1999Q12.072.075.228.750.506.25-1.54-0.41-13.33-1.2

1999Q23.633.635.132.310.806.25-1.54-0.41-13.33-1.2

1999Q33.613.615.47-3.481.306.25-1.54-0.41-13.33-1.2

1999Q43.913.916.0014.101.106.25-1.54-0.41-13.33-1.2

2000Q13.073.076.22-3.491.106.25-1.54-0.41-13.33-1.2

2000Q22.562.566.16-2.131.006.25-1.54-0.41-13.33-1.2

2000Q32.312.316.130.650.506.25-1.54-0.41-13.33-1.2

2000Q42.052.055.84-1.110.406.25-1.54-0.41-13.33-1.2

2001Q11.771.775.47-8.801.206.25-1.54-0.41-13.33-1.2

2001Q21.671.675.251.190.206.25-1.54-0.41-13.33-1.2

2001Q31.531.534.47-14.560.406.25-1.54-0.41-13.33-1.2

2001Q41.851.854.067.900.306.25-1.54-0.41-13.33-1.2

2002Q11.881.884.162.240.806.25-1.54-0.41-13.33-1.2

2002Q22.852.854.09-11.600.406.25-1.54-0.41-13.33-1.2

2002Q32.822.823.91-21.860.706.25-1.54-0.41-13.33-1.2

2002Q42.382.383.964.580.606.25-1.54-0.41-13.33-1.2

2003Q11.971.973.61-6.520.606.25-1.54-0.41-13.33-1.2

2003Q22.632.633.5913.560.906.25-1.54-0.41-13.33-1.2

2003Q32.782.783.673.820.706.25-1.54-0.41-13.33-1.2

2003Q43.273.273.989.000.906.25-1.54-0.41-13.33-1.2

2004Q13.433.434.330.621.006.25-1.54-0.41-13.33-1.2

2004Q24.814.814.792.170.606.25-1.54-0.41-13.33-1.2

2004Q34.244.244.862.830.106.25-1.54-0.41-13.33-1.2

2004Q44.824.824.846.460.806.25-1.54-0.41-13.33-1.2

2005Q12.642.644.933.000.306.25-1.54-0.41-13.33-1.2

2005Q24.394.394.734.890.706.25-1.54-0.41-13.33-1.2

2005Q34.324.324.557.850.606.25-1.54-0.41-13.33-1.2

2005Q45.905.904.594.180.706.25-1.54-0.41-13.33-1.2

2006Q14.354.354.567.781.106.25-1.54-0.41-13.33-1.2

2006Q24.944.944.73-1.850.406.25-1.54-0.41-13.33-1.2

2006Q33.653.655.053.580.506.25-1.54-0.41-13.33-1.2

2006Q43.703.705.295.970.806.25-1.54-0.41-13.33-1.2

2007Q12.232.235.582.870.706.25-1.54-0.41-13.33-1.2

2007Q22.082.085.984.440.606.25-1.54-0.41-13.33-1.2

2007Q3-1.02-1.026.28-1.780.506.25-1.54-0.41-13.33-1.2

2007Q4-8.93-8.935.95-0.350.506.25-1.54-0.41-13.33-1.2

2008Q1-3.44-3.446.02-10.370.706.25-1.54-0.41-13.33-1.2

2008Q2-2.70-2.705.94-1.46-0.106.25-1.54-0.41-13.33-1.2

2008Q3-4.89-4.896.30-12.99-0.706.25-1.54-0.41-13.33-1.2

2008Q4-14.51-14.512.83-10.74-1.806.25-1.54-0.41-13.33-1.2

Figure 1 & 3

IPD Returns

Figure 2

LIBOR

LIB REG

LIBOR Regime

Figure 4

FT Returns

FT REG

FT Returns Regime

Sheet2

GDP Growth

GDP REG

GDP Growth Regime

Sheet3

FT Returns

FT 1

FT2

FT Return Regimes (TAR-TAR)

IPD Returns

FT Returns

IPD versus FT Returns 1987-2008

IPD ReturnsAR-TARAR

1986Q4

1987Q12.44

1987Q22.723.047.48

1987Q34.957.4742.57

1987Q45.626.3716.88

1988Q15.204.72-1.92

1988Q28.0311.2255.86

1988Q37.266.40-5.71

1988Q46.696.04-3.04

1989Q14.792.65-27.22

1989Q25.175.6011.64

1989Q34.213.12-12.10

1989Q41.28-2.02-48.11

1990Q1-0.09-1.64-23.25

1990Q2-2.36-4.91-40.63

1990Q3-2.14-1.901.45

1990Q4-2.03-1.90-0.10

1991Q1-1.68-1.284.29

1991Q2-0.091.7126.77

1991Q3-0.05-0.010.55

1991Q41.062.3219.83

1992Q10.30-0.56-12.61

1992Q20.390.481.87

1992Q3-0.82-2.17-21.13

1992Q40.051.0314.73

1993Q10.831.7113.97

1993Q22.494.3630.49

1993Q33.835.3426.47

1993Q47.9512.5977.50

1994Q17.547.080.64

1994Q23.79-0.44-59.56

1994Q31.82-0.39-31.36

1994Q41.050.18-11.98

1995Q10.910.74-1.55

1995Q20.43-0.11-7.59

1995Q30.931.509.39

1995Q40.880.830.07

1996Q11.752.7216.34

1996Q22.092.477.84

1996Q32.082.061.86

1996Q43.034.1019.11

1997Q12.952.851.56

1997Q23.444.0011.78

1997Q33.433.433.34

1997Q44.535.7623.01

1998Q13.221.75-18.83

1998Q23.744.3312.52

1998Q32.801.73-13.16

1998Q41.700.47-16.77

1999Q12.072.488.25

1999Q23.635.3930.00

1999Q33.613.593.25

1999Q43.914.248.94

2000Q13.072.13-11.01

2000Q22.561.99-6.03

2000Q32.312.02-2.00

2000Q42.051.75-2.41

2001Q11.771.47-2.81

2001Q21.671.55-0.08

2001Q31.531.36-0.91

2001Q41.852.227.37

2002Q11.881.922.38

2002Q22.853.9519.26

2002Q32.822.792.29

2002Q42.381.88-5.10

2003Q11.971.50-5.00

2003Q22.633.3813.87

2003Q32.782.945.20

2003Q43.273.8411.68

2004Q13.433.616.10

2004Q24.816.3628.07

2004Q34.243.60-5.37

2004Q44.825.4814.70

2005Q12.640.17-34.34

2005Q24.396.3834.09

2005Q34.324.243.12

2005Q45.907.6832.51

2006Q14.352.61-21.75

2006Q24.945.6114.94

2006Q33.652.20-18.16

2006Q43.703.754.48

2007Q12.230.58-22.53

2007Q22.081.91-0.49

2007Q3-1.02-4.51-53.36

2007Q4-8.93-17.84-142.46

2008Q1-3.442.7589.19

2008Q2-2.70-1.869.87

2008Q3-4.89-7.36-41.86

2008Q4-14.51-25.36-177.01

2.141.92-1.15

3.274.8134.11

0.8130.5140.098

2.7249483.04222732097.475116

4.9526476867.465454016542.57331

5.61940240866.371490088316.8793354034

5.19769763954.7220220266-1.9239122868

8.02972611.224204518455.8560943604

7.2615376.3950332274-5.711397

6.6858616.0365085284-3.0359566212

4.79012632372.6517707251-27.2244224548

5.1729775.604825874911.6384325027

4.20709753043.1176023614-12.1043548584

1.2822022438-2.0170285449-48.11247

-0.08922204-1.6361646749-23.2493858337

-2.3555314541-4.9118888834-40.62822

-2.1429033279-1.9030625161.447891

-2.0286085606-1.8996860596-0.09843776

-1.6751872301-1.27653414324.293277

-0.085200851.708276011526.7659683228

-0.04989183-0.01006387220.5463953

1.06174767022.315657607319.83475

0.2975316346-0.5644907036-12.608297348

0.38536563520.48444085351.8686773777

-0.8175488-2.1744152693-21.1319732666

0.051432811.03162888614.7265090942

0.82941471.706964681513.9677171707

2.48747158054.357730777430.48819

3.8283055.340741674426.47186

7.94688212.592564909277.50005

7.5384467.07773732690.6409188509

3.7876107693-0.4432658482-59.55527

1.8224408627-0.3942364628-31.3647

1.05068171020.1801508681-11.9825344086

0.90526120.7412294048-1.550552

0.4303762-0.1052857843-7.589326

0.93106041.49582343129.386451

0.88311560.82903470310.073439315

1.74748122692.722470554616.3446044922

2.0883445742.4728324757.844733

2.07552838332.0610719441.8590914011

3.02768754964.101706456119.10744

2.9459092.85366422461.5648614168

3.439779523.996856839311.7801017761

3.4341895583.42788417853.339788

4.52856349955.762998187923.0099925995

3.2229151.7501663008-18.8264465332

3.7428964.329425484512.5241613388

2.79787468911.7319071588-13.1613349915

1.70380.4697028629-16.7725734711

2.06999516492.48305691388.25418

3.63149070745.392830401930.0015144348

3.6099013.58554818723.2453007698

3.9077874.24379720438.938385

3.0739436152.1333828429-11.0077285767

2.5647261.9903374258-6.034776

2.3092832.0211477583-2.004553

2.0453591.7476573384-2.4117052555

1.77402782441.4679709982-2.808121

1.67057728771.5538868894-0.07646142

1.5263150931.3635898576-0.9099388

1.85314834122.22181053577.372601

1.88252520561.91566179552.3786323071

2.85419869423.950229415419.2635

2.8223952.78652098852.2853043079

2.37972235681.8803953482-5.095986

1.96699237821.5014401723-5.0030565262

2.6325353.383255451113.872

2.7760963442.93803103225.2005133629

3.27403163913.835693953611.6829986572

3.4321493.6105026216.102383

4.80956840526.363273432228.0709762573

4.24031972893.5982171661-5.372961

4.8249244695.484348403514.6975336075

2.63518238070.1651915573-34.3444633484

4.39339637766.376631052134.08554

4.3223544.24221943913.1226115227

5.89810037617.675514761932.50879

4.35247755052.6090420034-21.74949646

4.9445225.612337796714.9427709579

3.6528842.1959388994-18.15987

3.6991793.75139895134.480998

2.2330381870.5792569618-22.52667

2.08086633681.9092191481-0.488962

-1.0184029341-4.514324531-53.3578453064

-8.925352-17.8442524211-142.4553222656

-3.44037866592.746575438889.18805

-2.696162-1.85669860149.871923

-4.885533-7.3551052422-41.8589057922

-14.50788-25.3617193248-177.0069122314

IPD Returns

AR-TAR

AR

2.7249483.0422273209

4.9526476867.4654540165

5.61940240866.3714900883

5.19769763954.7220220266

8.02972611.2242045184

7.2615376.3950332274

6.6858616.0365085284

4.79012632372.6517707251

5.1729775.6048258749

4.20709753043.1176023614

1.2822022438-2.0170285449

-0.08922204-1.6361646749

-2.3555314541-4.9118888834

-2.1429033279-1.903062516

-2.0286085606-1.8996860596

-1.6751872301-1.2765341432

-0.085200851.7082760115

-0.04989183-0.0100638722

1.06174767022.3156576073

0.2975316346-0.5644907036

0.38536563520.4844408535

-0.8175488-2.1744152693

0.051432811.031628886

0.82941471.7069646815

2.48747158054.3577307774

3.8283055.3407416744

7.94688212.5925649092

7.5384467.0777373269

3.7876107693-0.4432658482

1.8224408627-0.3942364628

1.05068171020.1801508681

0.90526120.7412294048

0.4303762-0.1052857843

0.93106041.4958234312

0.88311560.8290347031

1.74748122692.7224705546

2.0883445742.472832475

2.07552838332.061071944

3.02768754964.1017064561

2.9459092.8536642246

3.439779523.9968568393

3.4341895583.4278841785

4.52856349955.7629981879

3.2229151.7501663008

3.7428964.3294254845

2.79787468911.7319071588

1.70380.4697028629

2.06999516492.4830569138

3.63149070745.3928304019

3.6099013.5855481872

3.9077874.2437972043

3.0739436152.1333828429

2.5647261.9903374258

2.3092832.0211477583

2.0453591.7476573384

1.77402782441.4679709982

1.67057728771.5538868894

1.5263150931.3635898576

1.85314834122.2218105357

1.88252520561.9156617955

2.85419869423.9502294154

2.8223952.7865209885

2.37972235681.8803953482

1.96699237821.5014401723

2.6325353.3832554511

2.7760963442.9380310322

3.27403163913.8356939536

3.4321493.610502621

4.80956840526.3632734322

4.24031972893.5982171661

4.8249244695.4843484035

2.63518238070.1651915573

4.39339637766.3766310521

4.3223544.2422194391

5.89810037617.6755147619

4.35247755052.6090420034

4.9445225.6123377967

3.6528842.1959388994

3.6991793.7513989513

2.2330381870.5792569618

2.08086633681.9092191481

-1.0184029341-4.514324531

-8.925352-17.8442524211

-3.44037866592.7465754388

-2.696162-1.8566986014

-4.885533-7.3551052422

-14.50788-25.3617193248

IPD Returns

AR-TAR

IPD ReturnsTAR-TARARalpha 0.8

1986Q4

1987Q12.44

1987Q22.723.457.483.85

1987Q34.9510.6742.5713.86

1987Q45.627.3316.888.29

1988Q15.20-5.34-1.923.51

1988Q28.0315.3055.8619.36

1988Q37.265.29-5.714.19

1988Q46.695.21-3.044.38

1989Q14.79-0.08-27.22-2.79

1989Q25.176.1611.646.70

1989Q34.211.73-12.100.34

1989Q41.28-6.23-48.11-10.42

1990Q1-0.09-3.61-23.25-5.57

1990Q2-2.36-8.17-40.63-11.42

1990Q3-2.14-1.601.45-1.29

1990Q4-2.030.83-0.10-1.57

1991Q1-1.68-0.774.29-0.26

1991Q2-0.094.0026.776.27

1991Q3-0.050.040.550.09

1991Q41.063.9119.835.51

1992Q10.30-1.66-12.61-2.76

1992Q20.390.611.870.74

1992Q3-0.82-3.91-21.13-5.63

1992Q40.052.2814.733.53

1993Q10.832.8313.973.94

1993Q22.496.7430.499.12

1993Q33.837.2726.479.19

1993Q47.9518.5277.5024.42

1994Q17.546.490.645.90

1994Q23.79-5.84-59.56-11.22

1994Q31.82-3.22-31.36-6.04

1994Q41.05-0.93-11.98-2.04

1995Q10.910.53-1.550.32

1995Q20.43-0.79-7.59-1.47

1995Q30.932.229.392.93

1995Q40.880.760.070.69

1996Q11.753.9716.345.20

1996Q22.092.967.843.45

1996Q32.082.041.862.02

1996Q43.035.4719.116.84

1997Q12.952.741.562.62

1997Q23.444.7111.785.42

1997Q33.433.423.343.41

1997Q44.537.3423.018.91

1998Q13.22-0.13-18.83-2.00

1998Q23.745.0812.525.82

1998Q32.800.37-13.16-0.98

1998Q41.70-25.63-16.77-2.67

1999Q12.073.018.253.53

1999Q23.637.6430.009.88

1999Q33.613.553.253.52

1999Q43.914.678.945.10

2000Q13.070.93-11.01-0.26

2000Q22.561.26-6.030.53

2000Q32.311.65-2.001.29

2000Q42.051.37-2.410.99

2001Q11.771.08-2.810.69

2001Q21.671.41-0.081.26

2001Q31.531.16-0.910.95

2001Q41.8510.027.373.16

2002Q11.881.962.382.00

2002Q22.855.3519.266.74

2002Q32.822.742.292.70

2002Q42.38-8.68-5.100.61

2003Q11.970.91-5.000.32

2003Q22.634.3413.875.29

2003Q32.783.145.203.35

2003Q43.274.5511.685.27

2004Q13.433.846.104.06

2004Q24.818.3428.0710.32

2004Q34.242.78-5.371.96

2004Q44.826.3314.707.16

2005Q12.64-2.99-34.34-6.12

2005Q24.398.9134.0911.43

2005Q34.324.143.124.04

2005Q45.909.9432.5112.20

2006Q14.350.39-21.75-1.83

2006Q24.946.4614.947.31

2006Q33.650.34-18.16-1.51

2006Q43.703.824.483.88

2007Q12.23-1.53-22.53-3.63

2007Q22.081.69-0.491.47

2007Q3-1.02-8.97-53.36-13.42

2007Q4-8.93-29.22-142.46-40.55

2008Q1-3.4410.6489.1918.50

2008Q2-2.70-0.799.870.28

2008Q3-4.89-10.50-41.86-13.64

2008Q4-14.51-39.21-177.01-53.00

2.141.25-1.151.36

3.277.9534.119.82

0.8130.1990.0980.222

-1.999-2.514-2.154-2.721

8.06510.31010.84413.726

IPDTAR TARAR ARAlpha 0.8

IPD1.000

TAR TAR0.7371.000

AR AR0.6180.8891.000

Alpha 0.80.7620.9190.9801.000

2.62

-53.00

24.42

8.0318.5289.1924.42

-14.51-39.21-177.01-53.00

IPD Returns

TAR-TAR

AR

IPD Returns

TAR-TAR

alpha 0.8

IPD Returns

TAR-TAR

Smoothing and Underlying Return ProcessBasic Smoothing Model

Return Process

Note the Time Subscripts

Possible ModelsAR ModelAR return process, single smoothing parameterAR-TAR ModelRegime-based return, single smoothing processTAR-ARRegime-based smoothing, single return processTAR-TARRegime-based smoothing and return processes

Defining Regimes and ModellingRegime Variables TestedMacro: GDP, Employment, Inflation, /$Asset & Cap Market: Equity Market, Interest RateEndogenous: Cap RateAnalysis Quarterly, 1987Q1 2008Q4 Recursively Estimate and Minimise SSEBest Regime Models: AR-TARFT Returns, LIBORBest Regime Model: TAR-TARFT Returns for Both Processes

AR-TAR

Model

[Min,Max]

SSE

TAR

LIBOR

0.51**

(0.07)

-1.25*

(0.48)

1.27**

(0.10)

2.38**

(0.65)

0.18

(0.11)

6.25

0.56

[2.83,15.25]

233.45

Inflation rate

0.77**

(0.09)

0.25

(1.67)

-0.09

(0.15)

-0.22

(1.08)

0.95**

(0.23)

0.94

0.33

[-0.57,2.73]

259.44

Real interest

0.72**

(0.14)

-0.98

(0.75)

0.98**

(0.12)

3.01**

(1.13)

-0.17

(0.09)

5.12

0.57

[2.67,13.81]

242.68

FT returns

0.53**

(0.09)

2.22**

(0.32)

0.31**

(0.08)

-4.05**

(0.94)

1.77**

(0.24)

-1.54

0.76

[-32.00,18.84]

179.91

Exchange rate

0.93**

(0.02)

-40.54

(235.98)

1.70

(7.65)

1.33

(2.20)

0.02

(0.10)

1.95

0.05

[1.41,2.04]

240.19

Initial Yield

0.92**

(0.04)

1.60

(2.18)

0.02

(0.10)

-17.40**

(3.85)

1.76**

(0.32)

4.64

0.95

[4.57,9.09]

255.33

GDP Growth

0.81**

(0.12)

1.72

(0.99)

0.11

(0.08)

5.18

(6.66)

4.27*

(1.86)

-0.41

0.94

[-1.80,2.20]

208.52

AR

0.94**

(0.04)

-1.35

(2.82)

0.12

(0.15)

309.53

_1335081022.unknown

_1335081024.unknown

_1335081026.unknown

_1335081027.unknown

_1335081025.unknown

_1335081023.unknown

_1335081021.unknown

AR-TAR: FT Returns Regimes

Chart1

18.841917038-1.54

15.2607927322-1.54

5.616584-1.54

-32.0026550293-1.54

4.0549674034-1.54

8.310058-1.54

-0.4158257-1.54

-1.0190192461-1.54

15.8391513824-1.54

3.7536697388-1.54

7.152185-1.54

4.0634436607-1.54

-6.530186-1.54

6.268623-1.54

-18.13032341-1.54

8.147772-1.54

15.4552135468-1.54

-1.2575266361-1.54

10.16984272-1.54

-5.514645-1.54

-0.1393856108-1.54

5.096318-1.54

0.4986844361-1.54

13.169506073-1.54

4.48695-1.54

2.6163947582-1.54

6.1890354156-1.54

11.74033-1.54

-6.432471-1.54

-5.54714-1.54

4.34841-1.54

1.5851967335-1.54

2.368151-1.54

6.381937-1.54

7.720172-1.54

4.887479-1.54

3.473517-1.54

1.800711-1.54

5.992757-1.54

4.1683225632-1.54

5.147196-1.54

5.052799-1.54

12.3165931702-1.54

-1.3730785847-1.54

15.0943746567-1.54

-0.798896-1.54

-14.9692277908-1.54

13.5682315826-1.54

8.746055-1.54

2.3110244274-1.54

-3.4791407585-1.54

14.09605-1.54

-3.4921572208-1.54

-2.1302621365-1.54

0.6456831-1.54

-1.105868-1.54

-8.800473-1.54

1.1919534206-1.54

-14.55667-1.54

7.903409481-1.54

2.2446427345-1.54

-11.5977525711-1.54

-21.8640575409-1.54

4.577512-1.54

-6.516522-1.54

13.5642137527-1.54

3.8169956207-1.54

8.995739-1.54

0.6180823445-1.54

2.171329-1.54

2.8292126656-1.54

6.4608635902-1.54

3.003842-1.54

4.8901615143-1.54

7.847241-1.54

4.178603-1.54

7.783821-1.54

-1.8546527624-1.54

3.5838816166-1.54

5.97447-1.54

2.865909338-1.54

4.441267-1.54

-1.7781077623-1.54

-0.3495439-1.54

-10.37297-1.54

-1.4569555521-1.54

-12.993262291-1.54

-10.742609024-1.54

FT Returns

FT REG

FT Returns Regime

Figure 1 & 3


1986Q411.251.706.25-1.54-0.41-13.33-1.2LIBOR6.25FT1-13.33

1987Q12.442.4410.0018.840.506.25-1.54-0.41-13.33-1.2FT-1.54FT2-1.2

1987Q22.722.729.2515.261.106.25-1.54-0.41-13.33-1.2GDP-0.41

1987Q34.954.9510.385.622.206.25-1.54-0.41-13.33-1.2

1987Q45.625.628.94-32.000.906.25-1.54-0.41-13.33-1.2

1988Q15.205.208.694.051.706.25-1.54-0.41-13.33-1.2

1988Q28.038.039.888.310.506.25-1.54-0.41-13.33-1.2

1988Q37.267.2611.94-0.421.406.25-1.54-0.41-13.33-1.2

1988Q46.696.6913.25-1.020.706.25-1.54-0.41-13.33-1.2

1989Q14.794.7913.0615.840.406.25-1.54-0.41-13.33-1.2

1989Q25.175.1714.253.750.606.25-1.54-0.41-13.33-1.2

1989Q34.214.2114.697.150.106.25-1.54-0.41-13.33-1.2

1989Q41.281.2815.164.060.106.25-1.54-0.41-13.33-1.2

1990Q1-0.09-0.0915.25-6.530.806.25-1.54-0.41-13.33-1.2

1990Q2-2.36-2.3614.976.270.506.25-1.54-0.41-13.33-1.2

1990Q3-2.14-2.1414.97-18.13-1.206.25-1.54-0.41-13.33-1.2

1990Q4-2.03-2.0314.068.15-0.606.25-1.54-0.41-13.33-1.2

1991Q1-1.68-1.6812.4415.46-0.106.25-1.54-0.41-13.33-1.2

1991Q2-0.09-0.0911.31-1.26-0.306.25-1.54-0.41-13.33-1.2

1991Q3-0.05-0.0510.3410.17-0.406.25-1.54-0.41-13.33-1.2

1991Q41.061.0610.94-5.510.106.25-1.54-0.41-13.33-1.2

1992Q10.300.3010.81-0.140.106.25-1.54-0.41-13.33-1.2

1992Q20.390.3910.135.10-0.206.25-1.54-0.41-13.33-1.2

1992Q3-0.82-0.829.000.500.506.25-1.54-0.41-13.33-1.2

1992Q40.050.057.0013.170.606.25-1.54-0.41-13.33-1.2

1993Q10.830.835.944.490.606.25-1.54-0.41-13.33-1.2

1993Q22.492.495.972.620.506.25-1.54-0.41-13.33-1.2

1993Q33.833.836.006.190.906.25-1.54-0.41-13.33-1.2

1993Q47.957.955.3111.740.906.25-1.54-0.41-13.33-1.2

1994Q17.547.545.34-6.431.106.25-1.54-0.41-13.33-1.2

1994Q23.793.795.16-5.551.406.25-1.54-0.41-13.33-1.2

1994Q31.821.825.854.351.406.25-1.54-0.41-13.33-1.2

1994Q41.051.056.561.590.706.25-1.54-0.41-13.33-1.2

1995Q10.910.916.632.370.406.25-1.54-0.41-13.33-1.2

1995Q20.430.436.916.380.506.25-1.54-0.41-13.33-1.2

1995Q30.930.936.787.721.106.25-1.54-0.41-13.33-1.2

1995Q40.880.886.504.890.506.25-1.54-0.41-13.33-1.2

1996Q11.751.756.063.471.006.25-1.54-0.41-13.33-1.2

1996Q22.092.095.781.800.406.25-1.54-0.41-13.33-1.2

1996Q32.082.085.885.990.706.25-1.54-0.41-13.33-1.2

1996Q43.033.036.474.170.806.25-1.54-0.41-13.33-1.2

1997Q12.952.956.315.150.806.25-1.54-0.41-13.33-1.2

1997Q23.443.446.845.050.806.25-1.54-0.41-13.33-1.2

1997Q33.433.437.2512.321.006.25-1.54-0.41-13.33-1.2

1997Q44.534.537.56-1.371.206.25-1.54-0.41-13.33-1.2

1998Q13.223.227.5315.090.806.25-1.54-0.41-13.33-1.2

1998Q23.743.747.81-0.800.706.25-1.54-0.41-13.33-1.2

1998Q32.802.807.31-14.970.906.25-1.54-0.41-13.33-1.2

1998Q41.701.706.1913.571.106.25-1.54-0.41-13.33-1.2

1999Q12.072.075.228.750.506.25-1.54-0.41-13.33-1.2

1999Q23.633.635.132.310.806.25-1.54-0.41-13.33-1.2

1999Q33.613.615.47-3.481.306.25-1.54-0.41-13.33-1.2

1999Q43.913.916.0014.101.106.25-1.54-0.41-13.33-1.2

2000Q13.073.076.22-3.491.106.25-1.54-0.41-13.33-1.2

2000Q22.562.566.16-2.131.006.25-1.54-0.41-13.33-1.2

2000Q32.312.316.130.650.506.25-1.54-0.41-13.33-1.2

2000Q42.052.055.84-1.110.406.25-1.54-0.41-13.33-1.2

2001Q11.771.775.47-8.801.206.25-1.54-0.41-13.33-1.2

2001Q21.671.675.251.190.206.25-1.54-0.41-13.33-1.2

2001Q31.531.534.47-14.560.406.25-1.54-0.41-13.33-1.2

2001Q41.851.854.067.900.306.25-1.54-0.41-13.33-1.2

2002Q11.881.884.162.240.806.25-1.54-0.41-13.33-1.2

2002Q22.852.854.09-11.600.406.25-1.54-0.41-13.33-1.2

2002Q32.822.823.91-21.860.706.25-1.54-0.41-13.33-1.2

2002Q42.382.383.964.580.606.25-1.54-0.41-13.33-1.2

2003Q11.971.973.61-6.520.606.25-1.54-0.41-13.33-1.2

2003Q22.632.633.5913.560.906.25-1.54-0.41-13.33-1.2

2003Q32.782.783.673.820.706.25-1.54-0.41-13.33-1.2

2003Q43.273.273.989.000.906.25-1.54-0.41-13.33-1.2

2004Q13.433.434.330.621.006.25-1.54-0.41-13.33-1.2

2004Q24.814.814.792.170.606.25-1.54-0.41-13.33-1.2

2004Q34.244.244.862.830.106.25-1.54-0.41-13.33-1.2

2004Q44.824.824.846.460.806.25-1.54-0.41-13.33-1.2

2005Q12.642.644.933.000.306.25-1.54-0.41-13.33-1.2

2005Q24.394.394.734.890.706.25-1.54-0.41-13.33-1.2

2005Q34.324.324.557.850.606.25-1.54-0.41-13.33-1.2

2005Q45.905.904.594.180.706.25-1.54-0.41-13.33-1.2

2006Q14.354.354.567.781.106.25-1.54-0.41-13.33-1.2

2006Q24.944.944.73-1.850.406.25-1.54-0.41-13.33-1.2

2006Q33.653.655.053.580.506.25-1.54-0.41-13.33-1.2

2006Q43.703.705.295.970.806.25-1.54-0.41-13.33-1.2

2007Q12.232.235.582.870.706.25-1.54-0.41-13.33-1.2

2007Q22.082.085.984.440.606.25-1.54-0.41-13.33-1.2

2007Q3-1.02-1.026.28-1.780.506.25-1.54-0.41-13.33-1.2

2007Q4-8.93-8.935.95-0.350.506.25-1.54-0.41-13.33-1.2

2008Q1-3.44-3.446.02-10.370.706.25-1.54-0.41-13.33-1.2

2008Q2-2.70-2.705.94-1.46-0.106.25-1.54-0.41-13.33-1.2

2008Q3-4.89-4.896.30-12.99-0.706.25-1.54-0.41-13.33-1.2

2008Q4-14.51-14.512.83-10.74-1.806.25-1.54-0.41-13.33-1.2

Figure 1 & 3

IPD Returns

Figure 2

LIBOR

LIB REG

LIBOR Regime

Figure 4

FT Returns

FT REG

FT Returns Regime

Sheet2

GDP Growth

GDP REG

GDP Growth Regime

Sheet3

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

FT Returns

FT 1

FT2


IPD ReturnsAR-TARAR

1986Q4

1987Q12.44

1987Q22.723.047.48

1987Q34.957.4742.57

1987Q45.626.3716.88

1988Q15.204.72-1.92

1988Q28.0311.2255.86

1988Q37.266.40-5.71

1988Q46.696.04-3.04

1989Q14.792.65-27.22

1989Q25.175.6011.64

1989Q34.213.12-12.10

1989Q41.28-2.02-48.11

1990Q1-0.09-1.64-23.25

1990Q2-2.36-4.91-40.63

1990Q3-2.14-1.901.45

1990Q4-2.03-1.90-0.10

1991Q1-1.68-1.284.29

1991Q2-0.091.7126.77

1991Q3-0.05-0.010.55

1991Q41.062.3219.83

1992Q10.30-0.56-12.61

1992Q20.390.481.87

1992Q3-0.82-2.17-21.13

1992Q40.051.0314.73

1993Q10.831.7113.97

1993Q22.494.3630.49

1993Q33.835.3426.47

1993Q47.9512.5977.50

1994Q17.547.080.64

1994Q23.79-0.44-59.56

1994Q31.82-0.39-31.36

1994Q41.050.18-11.98

1995Q10.910.74-1.55

1995Q20.43-0.11-7.59

1995Q30.931.509.39

1995Q40.880.830.07

1996Q11.752.7216.34

1996Q22.092.477.84

1996Q32.082.061.86

1996Q43.034.1019.11

1997Q12.952.851.56

1997Q23.444.0011.78

1997Q33.433.433.34

1997Q44.535.7623.01

1998Q13.221.75-18.83

1998Q23.744.3312.52

1998Q32.801.73-13.16

1998Q41.700.47-16.77

1999Q12.072.488.25

1999Q23.635.3930.00

1999Q33.613.593.25

1999Q43.914.248.94

2000Q13.072.13-11.01

2000Q22.561.99-6.03

2000Q32.312.02-2.00

2000Q42.051.75-2.41

2001Q11.771.47-2.81

2001Q21.671.55-0.08

2001Q31.531.36-0.91

2001Q41.852.227.37

2002Q11.881.922.38

2002Q22.853.9519.26

2002Q32.822.792.29

2002Q42.381.88-5.10

2003Q11.971.50-5.00

2003Q22.633.3813.87

2003Q32.782.945.20

2003Q43.273.8411.68

2004Q13.433.616.10

2004Q24.816.3628.07

2004Q34.243.60-5.37

2004Q44.825.4814.70

2005Q12.640.17-34.34

2005Q24.396.3834.09

2005Q34.324.243.12

2005Q45.907.6832.51

2006Q14.352.61-21.75

2006Q24.945.6114.94

2006Q33.652.20-18.16

2006Q43.703.754.48

2007Q12.230.58-22.53

2007Q22.081.91-0.49

2007Q3-1.02-4.51-53.36

2007Q4-8.93-17.84-142.46

2008Q1-3.442.7589.19

2008Q2-2.70-1.869.87

2008Q3-4.89-7.36-41.86

2008Q4-14.51-25.36-177.01

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

000

IPD Returns

AR-TAR

AR


1986Q4

1987Q12.44

1987Q22.723.457.483.85

1987Q34.9510.6742.5713.86

1987Q45.627.3316.888.29

1988Q15.20-5.34-1.923.51

1988Q28.0315.3055.8619.36

1988Q37.265.29-5.714.19

1988Q46.695.21-3.044.38

1989Q14.79-0.08-27.22-2.79

1989Q25.176.1611.646.70

1989Q34.211.73-12.100.34

1989Q41.28-6.23-48.11-10.42

1990Q1-0.09-3.61-23.25-5.57

1990Q2-2.36-8.17-40.63-11.42

1990Q3-2.14-1.601.45-1.29

1990Q4-2.030.83-0.10-1.57

1991Q1-1.68-0.774.29-0.26

1991Q2-0.094.0026.776.27

1991Q3-0.050.040.550.09

1991Q41.063.9119.835.51

1992Q10.30-1.66-12.61-2.76

1992Q20.390.611.870.74

1992Q3-0.82-3.91-21.13-5.63

1992Q40.052.2814.733.53

1993Q10.832.8313.973.94

1993Q22.496.7430.499.12

1993Q33.837.2726.479.19

1993Q47.9518.5277.5024.42

1994Q17.546.490.645.90

1994Q23.79-5.84-59.56-11.22

1994Q31.82-3.22-31.36-6.04

1994Q41.05-0.93-11.98-2.04

1995Q10.910.53-1.550.32

1995Q20.43-0.79-7.59-1.47

1995Q30.932.229.392.93

1995Q40.880.760.070.69

1996Q11.753.9716.345.20

1996Q22.092.967.843.45

1996Q32.082.041.862.02

1996Q43.035.4719.116.84

1997Q12.952.741.562.62

1997Q23.444.7111.785.42

1997Q33.433.423.343.41

1997Q44.537.3423.018.91

1998Q13.22-0.13-18.83-2.00

1998Q23.745.0812.525.82

1998Q32.800.37-13.16-0.98

1998Q41.70-25.63-16.77-2.67

1999Q12.073.018.253.53

1999Q23.637.6430.009.88

1999Q33.613.553.253.52

1999Q43.914.678.945.10

2000Q13.070.93-11.01-0.26

2000Q22.561.26-6.030.53

2000Q32.311.65-2.001.29

2000Q42.051.37-2.410.99

2001Q11.771.08-2.810.69

2001Q21.671.41-0.081.26

2001Q31.531.16-0.910.95

2001Q41.8510.027.373.16

2002Q11.881.962.382.00

2002Q22.855.3519.266.74

2002Q32.822.742.292.70

2002Q42.38-8.68-5.100.61

2003Q11.970.91-5.000.32

2003Q22.634.3413.875.29

2003Q32.783.145.203.35

2003Q43.274.5511.685.27

2004Q13.433.846.104.06

2004Q24.818.3428.0710.32

2004Q34.242.78-5.371.96

2004Q44.826.3314.707.16

2005Q12.64-2.99-34.34-6.12

2005Q24.398.9134.0911.43

2005Q34.324.143.124.04

2005Q45.909.9432.5112.20

2006Q14.350.39-21.75-1.83

2006Q24.946.4614.947.31

2006Q33.650.34-18.16-1.51

2006Q43.703.824.483.88

2007Q12.23-1.53-22.53-3.63

2007Q22.081.69-0.491.47

2007Q3-1.02-8.97-53.36-13.42

2007Q4-8.93-29.22-142.46-40.55

2008Q1-3.4410.6489.1918.50

2008Q2-2.70-0.799.870.28

2008Q3-4.89-10.50-41.86-13.64

2008Q4-14.51-39.21-177.01-53.00

2.141.25-1.151.36

3.277.9534.119.82

0.8130.1990.0980.222

-1.999-2.514-2.154-2.721

8.06510.31010.84413.726


IPD1.000

TAR TAR0.7371.000

AR AR0.6180.8891.000

Alpha 0.80.7620.9190.9801.000

2.62

-53.00

24.42

IPD Returns

TAR-TAR

AR

IPD Returns

TAR-TAR

alpha 0.8

IPD Returns

TAR-TAR

AR-TAR versus AR: Fits The AR model appears too volatile particularly across 2008 The AR-TAR model generates more plausible results

Chart5

2.7249483.04222732097.475116

4.9526476867.465454016542.57331

5.61940240866.371490088316.8793354034

5.19769763954.7220220266-1.9239122868

8.02972611.224204518455.8560943604

7.2615376.3950332274-5.711397

6.6858616.0365085284-3.0359566212

4.79012632372.6517707251-27.2244224548

5.1729775.604825874911.6384325027

4.20709753043.1176023614-12.1043548584

1.2822022438-2.0170285449-48.11247

-0.08922204-1.6361646749-23.2493858337

-2.3555314541-4.9118888834-40.62822

-2.1429033279-1.9030625161.447891

-2.0286085606-1.8996860596-0.09843776

-1.6751872301-1.27653414324.293277

-0.085200851.708276011526.7659683228

-0.04989183-0.01006387220.5463953

1.06174767022.315657607319.83475

0.2975316346-0.5644907036-12.608297348

0.38536563520.48444085351.8686773777

-0.8175488-2.1744152693-21.1319732666

0.051432811.03162888614.7265090942

0.82941471.706964681513.9677171707

2.48747158054.357730777430.48819

3.8283055.340741674426.47186

7.94688212.592564909277.50005

7.5384467.07773732690.6409188509

3.7876107693-0.4432658482-59.55527

1.8224408627-0.3942364628-31.3647

1.05068171020.1801508681-11.9825344086

0.90526120.7412294048-1.550552

0.4303762-0.1052857843-7.589326

0.93106041.49582343129.386451

0.88311560.82903470310.073439315

1.74748122692.722470554616.3446044922

2.0883445742.4728324757.844733

2.07552838332.0610719441.8590914011

3.02768754964.101706456119.10744

2.9459092.85366422461.5648614168

3.439779523.996856839311.7801017761

3.4341895583.42788417853.339788

4.52856349955.762998187923.0099925995

3.2229151.7501663008-18.8264465332

3.7428964.329425484512.5241613388

2.79787468911.7319071588-13.1613349915

1.70380.4697028629-16.7725734711

2.06999516492.48305691388.25418

3.63149070745.392830401930.0015144348

3.6099013.58554818723.2453007698

3.9077874.24379720438.938385

3.0739436152.1333828429-11.0077285767

2.5647261.9903374258-6.034776

2.3092832.0211477583-2.004553

2.0453591.7476573384-2.4117052555

1.77402782441.4679709982-2.808121

1.67057728771.5538868894-0.07646142

1.5263150931.3635898576-0.9099388

1.85314834122.22181053577.372601

1.88252520561.91566179552.3786323071

2.85419869423.950229415419.2635

2.8223952.78652098852.2853043079

2.37972235681.8803953482-5.095986

1.96699237821.5014401723-5.0030565262

2.6325353.383255451113.872

2.7760963442.93803103225.2005133629

3.27403163913.835693953611.6829986572

3.4321493.6105026216.102383

4.80956840526.363273432228.0709762573

4.24031972893.5982171661-5.372961

4.8249244695.484348403514.6975336075

2.63518238070.1651915573-34.3444633484

4.39339637766.376631052134.08554

4.3223544.24221943913.1226115227

5.89810037617.675514761932.50879

4.35247755052.6090420034-21.74949646

4.9445225.612337796714.9427709579

3.6528842.1959388994-18.15987

3.6991793.75139895134.480998

2.2330381870.5792569618-22.52667

2.08086633681.9092191481-0.488962

-1.0184029341-4.514324531-53.3578453064

-8.925352-17.8442524211-142.4553222656

-3.44037866592.746575438889.18805

-2.696162-1.85669860149.871923

-4.885533-7.3551052422-41.8589057922

-14.50788-25.3617193248-177.0069122314

IPD Returns

AR-TAR

AR

Figure 1 & 3


1986Q411.251.706.25-1.54-0.41-13.33-1.2LIBOR6.25FT1-13.33

1987Q12.442.4410.0018.840.506.25-1.54-0.41-13.33-1.2FT-1.54FT2-1.2

1987Q22.722.729.2515.261.106.25-1.54-0.41-13.33-1.2GDP-0.41

1987Q34.954.9510.385.622.206.25-1.54-0.41-13.33-1.2

1987Q45.625.628.94-32.000.906.25-1.54-0.41-13.33-1.2

1988Q15.205.208.694.051.706.25-1.54-0.41-13.33-1.2

1988Q28.038.039.888.310.506.25-1.54-0.41-13.33-1.2

1988Q37.267.2611.94-0.421.406.25-1.54-0.41-13.33-1.2

1988Q46.696.6913.25-1.020.706.25-1.54-0.41-13.33-1.2

1989Q14.794.7913.0615.840.406.25-1.54-0.41-13.33-1.2

1989Q25.175.1714.253.750.606.25-1.54-0.41-13.33-1.2

1989Q34.214.2114.697.150.106.25-1.54-0.41-13.33-1.2

1989Q41.281.2815.164.060.106.25-1.54-0.41-13.33-1.2

1990Q1-0.09-0.0915.25-6.530.806.25-1.54-0.41-13.33-1.2

1990Q2-2.36-2.3614.976.270.506.25-1.54-0.41-13.33-1.2

1990Q3-2.14-2.1414.97-18.13-1.206.25-1.54-0.41-13.33-1.2

1990Q4-2.03-2.0314.068.15-0.606.25-1.54-0.41-13.33-1.2

1991Q1-1.68-1.6812.4415.46-0.106.25-1.54-0.41-13.33-1.2

1991Q2-0.09-0.0911.31-1.26-0.306.25-1.54-0.41-13.33-1.2

1991Q3-0.05-0.0510.3410.17-0.406.25-1.54-0.41-13.33-1.2

1991Q41.061.0610.94-5.510.106.25-1.54-0.41-13.33-1.2

1992Q10.300.3010.81-0.140.106.25-1.54-0.41-13.33-1.2

1992Q20.390.3910.135.10-0.206.25-1.54-0.41-13.33-1.2

1992Q3-0.82-0.829.000.500.506.25-1.54-0.41-13.33-1.2

1992Q40.050.057.0013.170.606.25-1.54-0.41-13.33-1.2

1993Q10.830.835.944.490.606.25-1.54-0.41-13.33-1.2

1993Q22.492.495.972.620.506.25-1.54-0.41-13.33-1.2

1993Q33.833.836.006.190.906.25-1.54-0.41-13.33-1.2

1993Q47.957.955.3111.740.906.25-1.54-0.41-13.33-1.2

1994Q17.547.545.34-6.431.106.25-1.54-0.41-13.33-1.2

1994Q23.793.795.16-5.551.406.25-1.54-0.41-13.33-1.2

1994Q31.821.825.854.351.406.25-1.54-0.41-13.33-1.2

1994Q41.051.056.561.590.706.25-1.54-0.41-13.33-1.2

1995Q10.910.916.632.370.406.25-1.54-0.41-13.33-1.2

1995Q20.430.436.916.380.506.25-1.54-0.41-13.33-1.2

1995Q30.930.936.787.721.106.25-1.54-0.41-13.33-1.2

1995Q40.880.886.504.890.506.25-1.54-0.41-13.33-1.2

1996Q11.751.756.063.471.006.25-1.54-0.41-13.33-1.2

1996Q22.092.095.781.800.406.25-1.54-0.41-13.33-1.2

1996Q32.082.085.885.990.706.25-1.54-0.41-13.33-1.2

1996Q43.033.036.474.170.806.25-1.54-0.41-13.33-1.2

1997Q12.952.956.315.150.806.25-1.54-0.41-13.33-1.2

1997Q23.443.446.845.050.806.25-1.54-0.41-13.33-1.2

1997Q33.433.437.2512.321.006.25-1.54-0.41-13.33-1.2

1997Q44.534.537.56-1.371.206.25-1.54-0.41-13.33-1.2

1998Q13.223.227.5315.090.806.25-1.54-0.41-13.33-1.2

1998Q23.743.747.81-0.800.706.25-1.54-0.41-13.33-1.2

1998Q32.802.807.31-14.970.906.25-1.54-0.41-13.33-1.2

1998Q41.701.706.1913.571.106.25-1.54-0.41-13.33-1.2

1999Q12.072.075.228.750.506.25-1.54-0.41-13.33-1.2

1999Q23.633.635.132.310.806.25-1.54-0.41-13.33-1.2

1999Q33.613.615.47-3.481.306.25-1.54-0.41-13.33-1.2

1999Q43.913.916.0014.101.106.25-1.54-0.41-13.33-1.2

2000Q13.073.076.22-3.491.106.25-1.54-0.41-13.33-1.2

2000Q22.562.566.16-2.131.006.25-1.54-0.41-13.33-1.2

2000Q32.312.316.130.650.506.25-1.54-0.41-13.33-1.2

2000Q42.052.055.84-1.110.406.25-1.54-0.41-13.33-1.2

2001Q11.771.775.47-8.801.206.25-1.54-0.41-13.33-1.2

2001Q21.671.675.251.190.206.25-1.54-0.41-13.33-1.2

2001Q31.531.534.47-14.560.406.25-1.54-0.41-13.33-1.2

2001Q41.851.854.067.900.306.25-1.54-0.41-13.33-1.2

2002Q11.881.884.162.240.806.25-1.54-0.41-13.33-1.2

2002Q22.852.854.09-11.600.406.25-1.54-0.41-13.33-1.2

2002Q32.822.823.91-21.860.706.25-1.54-0.41-13.33-1.2

2002Q42.382.383.964.580.606.25-1.54-0.41-13.33-1.2

2003Q11.971.973.61-6.520.606.25-1.54-0.41-13.33-1.2

2003Q22.632.633.5913.560.906.25-1.54-0.41-13.33-1.2

2003Q32.782.783.673.820.706.25-1.54-0.41-13.33-1.2

2003Q43.273.273.989.000.906.25-1.54-0.41-13.33-1.2

2004Q13.433.434.330.621.006.25-1.54-0.41-13.33-1.2

2004Q24.814.814.792.170.606.25-1.54-0.41-13.33-1.2

2004Q34.244.244.862.830.106.25-1.54-0.41-13.33-1.2

2004Q44.824.824.846.460.806.25-1.54-0.41-13.33-1.2

2005Q12.642.644.933.000.306.25-1.54-0.41-13.33-1.2

2005Q24.394.394.734.890.706.25-1.54-0.41-13.33-1.2

2005Q34.324.324.557.850.606.25-1.54-0.41-13.33-1.2

2005Q45.905.904.594.180.706.25-1.54-0.41-13.33-1.2

2006Q14.354.354.567.781.106.25-1.54-0.41-13.33-1.2

2006Q24.944.944.73-1.850.406.25-1.54-0.41-13.33-1.2

2006Q33.653.655.053.580.506.25-1.54-0.41-13.33-1.2

2006Q43.703.705.295.970.806.25-1.54-0.41-13.33-1.2

2007Q12.232.235.582.870.706.25-1.54-0.41-13.33-1.2

2007Q22.082.085.984.440.606.25-1.54-0.41-13.33-1.2

2007Q3-1.02-1.026.28-1.780.506.25-1.54-0.41-13.33-1.2

2007Q4-8.93-8.935.95-0.350.506.25-1.54-0.41-13.33-1.2

2008Q1-3.44-3.446.02-10.370.706.25-1.54-0.41-13.33-1.2

2008Q2-2.70-2.705.94-1.46-0.106.25-1.54-0.41-13.33-1.2

2008Q3-4.89-4.896.30-12.99-0.706.25-1.54-0.41-13.33-1.2

2008Q4-14.51-14.512.83-10.74-1.806.25-1.54-0.41-13.33-1.2

Figure 1 & 3

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IPD Returns

Figure 2

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LIBOR

LIB REG

LIBOR Regime

Figure 4

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FT Returns

FT REG

FT Returns Regime

Sheet2

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GDP Growth

GDP REG

GDP Growth Regime

Sheet3

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FT Returns

FT 1

FT2


IPD ReturnsAR-TARAR

1986Q4

1987Q12.44

1987Q22.723.047.48

1987Q34.957.4742.57

1987Q45.626.3716.88

1988Q15.204.72-1.92

1988Q28.0311.2255.86

1988Q37.266.40-5.71

1988Q46.696.04-3.04

1989Q14.792.65-27.22

1989Q25.175.6011.64

1989Q34.213.12-12.10

1989Q41.28-2.02-48.11

1990Q1-0.09-1.64-23.25

1990Q2-2.36-4.91-40.63

1990Q3-2.14-1.901.45

1990Q4-2.03-1.90-0.10

1991Q1-1.68-1.284.29

1991Q2-0.091.7126.77

1991Q3-0.05-0.010.55

1991Q41.062.3219.83

1992Q10.30-0.56-12.61

1992Q20.390.481.87

1992Q3-0.82-2.17-21.13

1992Q40.051.0314.73

1993Q10.831.7113.97

1993Q22.494.3630.49

1993Q33.835.3426.47

1993Q47.9512.5977.50

1994Q17.547.080.64

1994Q23.79-0.44-59.56

1994Q31.82-0.39-31.36

1994Q41.050.18-11.98

1995Q10.910.74-1.55

1995Q20.43-0.11-7.59

1995Q30.931.509.39

1995Q40.880.830.07

1996Q11.752.7216.34

1996Q22.092.477.84

1996Q32.082.061.86

1996Q43.034.1019.11

1997Q12.952.851.56

1997Q23.444.0011.78

1997Q33.433.433.34

1997Q44.535.7623.01

1998Q13.221.75-18.83

1998Q23.744.3312.52

1998Q32.801.73-13.16

1998Q41.700.47-16.77

1999Q12.072.488.25

1999Q23.635.3930.00

1999Q33.613.593.25

1999Q43.914.248.94

2000Q13.072.13-11.01

2000Q22.561.99-6.03

2000Q32.312.02-2.00

2000Q42.051.75-2.41

2001Q11.771.47-2.81

2001Q21.671.55-0.08

2001Q31.531.36-0.91

2001Q41.852.227.37

2002Q11.881.922.38

2002Q22.853.9519.26

2002Q32.822.792.29

2002Q42.381.88-5.10

2003Q11.971.50-5.00

2003Q22.633.3813.87

2003Q32.782.945.20

2003Q43.273.8411.68

2004Q13.433.616.10

2004Q24.816.3628.07

2004Q34.243.60-5.37

2004Q44.825.4814.70

2005Q12.640.17-34.34

2005Q24.396.3834.09

2005Q34.324.243.12

2005Q45.907.6832.51

2006Q14.352.61-21.75

2006Q24.945.6114.94

2006Q33.652.20-18.16

2006Q43.703.754.48

2007Q12.230.58-22.53

2007Q22.081.91-0.49

2007Q3-1.02-4.51-53.36

2007Q4-8.93-17.84-142.46

2008Q1-3.442.7589.19

2008Q2-2.70-1.869.87

2008Q3-4.89-7.36-41.86

2008Q4-14.51-25.36-177.01

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IPD Returns

AR-TAR

AR

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IPD Returns

AR-TAR


1986Q4

1987Q12.44

1987Q22.723.457.483.85

1987Q34.9510.6742.5713.86

1987Q45.627.3316.888.29

1988Q15.20-5.34-1.923.51

1988Q28.0315.3055.8619.36

1988Q37.265.29-5.714.19

1988Q46.695.21-3.044.38

1989Q14.79-0.08-27.22-2.79

1989Q25.176.1611.646.70

1989Q34.211.73-12.100.34

1989Q41.28-6.23-48.11-10.42

1990Q1-0.09-3.61-23.25-5.57

1990Q2-2.36-8.17-40.63-11.42

1990Q3-2.14-1.601.45-1.29

1990Q4-2.030.83-0.10-1.57

1991Q1-1.68-0.774.29-0.26

1991Q2-0.094.0026.776.27

1991Q3-0.050.040.550.09

1991Q41.063.9119.835.51

1992Q10.30-1.66-12.61-2.76

1992Q20.390.611.870.74

1992Q3-0.82-3.91-21.13-5.63

1992Q40.052.2814.733.53

1993Q10.832.8313.973.94

1993Q22.496.7430.499.12

1993Q33.837.2726.479.19

1993Q47.9518.5277.5024.42

1994Q17.546.490.645.90

1994Q23.79-5.84-59.56-11.22

1994Q31.82-3.22-31.36-6.04

1994Q41.05-0.93-11.98-2.04

1995Q10.910.53-1.550.32

1995Q20.43-0.79-7.59-1.47

1995Q30.932.229.392.93

1995Q40.880.760.070.69

1996Q11.753.9716.345.20

1996Q22.092.967.843.45

1996Q32.082.041.862.02

1996Q43.035.4719.116.84

1997Q12.952.741.562.62

1997Q23.444.7111.785.42

1997Q33.433.423.343.41

1997Q44.537.3423.018.91

1998Q13.22-0.13-18.83-2.00

1998Q23.745.0812.525.82

1998Q32.800.37-13.16-0.98

1998Q41.70-25.63-16.77-2.67

1999Q12.073.018.253.53

1999Q23.637.6430.009.88

1999Q33.613.553.253.52

1999Q43.914.678.945.10

2000Q13.070.93-11.01-0.26

2000Q22.561.26-6.030.53

2000Q32.311.65-2.001.29

2000Q42.051.37-2.410.99

2001Q11.771.08-2.810.69

2001Q21.671.41-0.081.26

2001Q31.531.16-0.910.95

2001Q41.8510.027.373.16

2002Q11.881.962.382.00

2002Q22.855.3519.266.74

2002Q32.822.742.292.70

2002Q42.38-8.68-5.100.61

2003Q11.970.91-5.000.32

2003Q22.634.3413.875.29

2003Q32.783.145.203.35

2003Q43.274.5511.685.27

2004Q13.433.846.104.06

2004Q24.818.3428.0710.32

2004Q34.242.78-5.371.96

2004Q44.826.3314.707.16

2005Q12.64-2.99-34.34-6.12

2005Q24.398.9134.0911.43

2005Q34.324.143.124.04

2005Q45.909.9432.5112.20

2006Q14.350.39-21.75-1.83

2006Q24.946.4614.947.31

2006Q33.650.34-18.16-1.51

2006Q43.703.824.483.88

2007Q12.23-1.53-22.53-3.63

2007Q22.081.69-0.491.47

2007Q3-1.02-8.97-53.36-13.42

2007Q4-8.93-29.22-142.46-40.55

2008Q1-3.4410.6489.1918.50

2008Q2-2.70-0.799.870.28

2008Q3-4.89-10.50-41.86-13.64

2008Q4-14.51-39.21-177.01-53.00

2.141.25-1.151.36

3.277.9534.119.82

0.8130.1990.0980.222

-1.999-2.514-2.154-2.721

8.06510.31010.84413.726


IPD1.000

TAR TAR0.7371.000

AR AR0.6180.8891.000

Alpha 0.80.7620.9190.9801.000

2.62

-53.00

24.42

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IPD Returns

TAR-TAR

AR

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IPD Returns

TAR-TAR

alpha 0.8

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IPD Returns

TAR-TAR

AR-TAR versus AR: Fits The AR model appears too volatile particularly across 2008 The AR-TAR model generates more plausible results Still seems rather smoothed Standard deviation compared to IPD 4.8% (3.1%) Serial correlation 0.51 (0.81)

Chart6

2.7249483.0422273209

4.9526476867.4654540165

5.61940240866.3714900883

5.19769763954.7220220266

8.02972611.2242045184

7.2615376.3950332274

6.6858616.0365085284

4.79012632372.6517707251

5.1729775.6048258749

4.20709753043.1176023614

1.2822022438-2.0170285449

-0.08922204-1.6361646749

-2.3555314541-4.9118888834

-2.1429033279-1.903062516

-2.0286085606-1.8996860596

-1.6751872301-1.2765341432

-0.085200851.7082760115

-0.04989183-0.0100638722

1.06174767022.3156576073

0.2975316346-0.5644907036

0.38536563520.4844408535

-0.8175488-2.1744152693

0.051432811.031628886

0.82941471.7069646815

2.48747158054.3577307774

3.8283055.3407416744

7.94688212.5925649092

7.5384467.0777373269

3.7876107693-0.4432658482

1.8224408627-0.3942364628

1.05068171020.1801508681

0.90526120.7412294048

0.4303762-0.1052857843

0.93106041.4958234312

0.88311560.8290347031

1.74748122692.7224705546

2.0883445742.472832475

2.07552838332.061071944

3.02768754964.1017064561

2.9459092.8536642246

3.439779523.9968568393

3.4341895583.4278841785

4.52856349955.7629981879

3.2229151.7501663008

3.7428964.3294254845

2.79787468911.7319071588

1.70380.4697028629

2.06999516492.4830569138

3.63149070745.3928304019

3.6099013.5855481872

3.9077874.2437972043

3.0739436152.1333828429

2.5647261.9903374258

2.3092832.0211477583

2.0453591.7476573384

1.77402782441.4679709982

1.67057728771.5538868894

1.5263150931.3635898576

1.85314834122.2218105357

1.88252520561.9156617955

2.85419869423.9502294154

2.8223952.7865209885

2.37972235681.8803953482

1.96699237821.5014401723

2.6325353.3832554511

2.7760963442.9380310322

3.27403163913.8356939536

3.4321493.610502621

4.80956840526.3632734322

4.24031972893.5982171661

4.8249244695.4843484035

2.63518238070.1651915573

4.39339637766.3766310521

4.3223544.2422194391

5.89810037617.6755147619

4.35247755052.6090420034

4.9445225.6123377967

3.6528842.1959388994

3.6991793.7513989513

2.2330381870.5792569618

2.08086633681.9092191481

-1.0184029341-4.514324531

-8.925352-17.8442524211

-3.44037866592.7465754388

-2.696162-1.8566986014

-4.885533-7.3551052422

-14.50788-25.3617193248

IPD Returns

AR-TAR

Figure 1 & 3


1986Q411.251.706.25-1.54-0.41-13.33-1.2LIBOR6.25FT1-13.33

1987Q12.442.4410.0018.840.506.25-1.54-0.41-13.33-1.2FT-1.54FT2-1.2

1987Q22.722.729.2515.261.106.25-1.54-0.41-13.33-1.2GDP-0.41

1987Q34.954.9510.385.622.206.25-1.54-0.41-13.33-1.2

1987Q45.625.628.94-32.000.906.25-1.54-0.41-13.33-1.2

1988Q15.205.208.694.051.706.25-1.54-0.41-13.33-1.2

1988Q28.038.039.888.310.506.25-1.54-0.41-13.33-1.2

1988Q37.267.2611.94-0.421.406.25-1.54-0.41-13.33-1.2

1988Q46.696.6913.25-1.020.706.25-1.54-0.41-13.33-1.2

1989Q14.794.7913.0615.840.406.25-1.54-0.41-13.33-1.2

1989Q25.175.1714.253.750.606.25-1.54-0.41-13.33-1.2

1989Q34.214.2114.697.150.106.25-1.54-0.41-13.33-1.2

1989Q41.281.2815.164.060.106.25-1.54-0.41-13.33-1.2

1990Q1-0.09-0.0915.25-6.530.806.25-1.54-0.41-13.33-1.2

1990Q2-2.36-2.3614.976.270.506.25-1.54-0.41-13.33-1.2

1990Q3-2.14-2.1414.97-18.13-1.206.25-1.54-0.41-13.33-1.2

1990Q4-2.03-2.0314.068.15-0.606.25-1.54-0.41-13.33-1.2

1991Q1-1.68-1.6812.4415.46-0.106.25-1.54-0.41-13.33-1.2

1991Q2-0.09-0.0911.31-1.26-0.306.25-1.54-0.41-13.33-1.2

1991Q3-0.05-0.0510.3410.17-0.406.25-1.54-0.41-13.33-1.2

1991Q41.061.0610.94-5.510.106.25-1.54-0.41-13.33-1.2

1992Q10.300.3010.81-0.140.106.25-1.54-0.41-13.33-1.2

1992Q20.390.3910.135.10-0.206.25-1.54-0.41-13.33-1.2

1992Q3-0.82-0.829.000.500.506.25-1.54-0.41-13.33-1.2

1992Q40.050.057.0013.170.606.25-1.54-0.41-13.33-1.2

1993Q10.830.835.944.490.606.25-1.54-0.41-13.33-1.2

1993Q22.492.495.972.620.506.25-1.54-0.41-13.33-1.2

1993Q33.833.836.006.190.906.25-1.54-0.41-13.33-1.2

1993Q47.957.955.3111.740.906.25-1.54-0.41-13.33-1.2

1994Q17.547.545.34-6.431.106.25-1.54-0.41-13.33-1.2

1994Q23.793.795.16-5.551.406.25-1.54-0.41-13.33-1.2

1994Q31.821.825.854.351.406.25-1.54-0.41-13.33-1.2

1994Q41.051.056.561.590.706.25-1.54-0.41-13.33-1.2

1995Q10.910.916.632.370.406.25-1.54-0.41-13.33-1.2

1995Q20.430.436.916.380.506.25-1.54-0.41-13.33-1.2

1995Q30.930.936.787.721.106.25-1.54-0.41-13.33-1.2

1995Q40.880.886.504.890.506.25-1.54-0.41-13.33-1.2

1996Q11.751.756.063.471.006.25-1.54-0.41-13.33-1.2

1996Q22.092.095.781.800.406.25-1.54-0.41-13.33-1.2

1996Q32.082.085.885.990.706.25-1.54-0.41-13.33-1.2

1996Q43.033.036.474.170.806.25-1.54-0.41-13.33-1.2

1997Q12.952.956.315.150.806.25-1.54-0.41-13.33-1.2

1997Q23.443.446.845.050.806.25-1.54-0.41-13.33-1.2

1997Q33.433.437.2512.321.006.25-1.54-0.41-13.33-1.2

1997Q44.534.537.56-1.371.206.25-1.54-0.41-13.33-1.2

1998Q13.223.227.5315.090.806.25-1.54-0.41-13.33-1.2

1998Q23.743.747.81-0.800.706.25-1.54-0.41-13.33-1.2

1998Q32.802.807.31-14.970.906.25-1.54-0.41-13.33-1.2

1998Q41.701.706.1913.571.106.25-1.54-0.41-13.33-1.2

1999Q12.072.075.228.750.506.25-1.54-0.41-13.33-1.2

1999Q23.633.635.132.310.806.25-1.54-0.41-13.33-1.2

1999Q33.613.615.47-3.481.306.25-1.54-0.41-13.33-1.2

1999Q43.913.916.0014.101.106.25-1.54-0.41-13.33-1.2

2000Q13.073.076.22-3.491.106.25-1.54-0.41-13.33-1.2

2000Q22.562.566.16-2.131.006.25-1.54-0.41-13.33-1.2

2000Q32.312.316.130.650.506.25-1.54-0.41-13.33-1.2

2000Q42.052.055.84-1.110.406.25-1.54-0.41-13.33-1.2

2001Q11.771.775.47-8.801.206.25-1.54-0.41-13.33-1.2

2001Q21.671.675.251.190.206.25-1.54-0.41-13.33-1.2

2001Q31.531.534.47-14.560.406.25-1.54-0.41-13.33-1.2

2001Q41.851.854.067.900.306.25-1.54-0.41-13.33-1.2

2002Q11.881.884.162.240.806.25-1.54-0.41-13.33-1.2

2002Q22.852.854.09-11.600.406.25-1.54-0.41-13.33-1.2

2002Q32.822.823.91-21.860.706.25-1.54-0.41-13.33-1.2

2002Q42.382.383.964.580.606.25-1.54-0.41-13.33-1.2

2003Q11.971.973.61-6.520.606.25-1.54-0.41-13.33-1.2

2003Q22.632.633.5913.560.906.25-1.54-0.41-13.33-1.2

2003Q32.782.783.673.820.706.25-1.54-0.41-13.33-1.2

2003Q43.273.273.989.000.906.25-1.54-0.41-13.33-1.2

2004Q13.433.434.330.621.006.25-1.54-0.41-13.33-1.2

2004Q24.814.814.792.170.606.25-1.54-0.41-13.33-1.2

2004Q34.244.244.862.830.106.25-1.54-0.41-13.33-1.2

2004Q44.824.824.846.460.806.25-1.54-0.41-13.33-1.2

2005Q12.642.644.933.000.306.25-1.54-0.41-13.33-1.2

2005Q24.394.394.734.890.706.25-1.54-0.41-13.33-1.2

2005Q34.324.324.557.850.606.25-1.54-0.41-13.33-1.2

2005Q45.905.904.594.180.706.25-1.54-0.41-13.33-1.2

2006Q14.354.354.567.781.106.25-1.54-0.41-13.33-1.2

2006Q24.944.944.73-1.850.406.25-1.54-0.41-13.33-1.2

2006Q33.653.655.053.580.506.25-1.54-0.41-13.33-1.2

2006Q43.703.705.295.970.806.25-1.54-0.41-13.33-1.2

2007Q12.232.235.582.870.706.25-1.54-0.41-13.33-1.2

2007Q22.082.085.984.440.606.25-1.54-0.41-13.33-1.2

2007Q3-1.02-1.026.28-1.780.506.25-1.54-0.41-13.33-1.2

2007Q4-8.93-8.935.95-0.350.506.25-1.54-0.41-13.33-1.2

2008Q1-3.44-3.446.02-10.370.706.25-1.54-0.41-13.33-1.2

2008Q2-2.70-2.705.94-1.46-0.106.25-1.54-0.41-13.33-1.2

2008Q3-4.89-4.896.30-12.99-0.706.25-1.54-0.41-13.33-1.2

2008Q4-14.51-14.512.83-10.74-1.806.25-1.54-0.41-13.33-1.2

Figure 1 & 3

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IPD Returns

Figure 2

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LIBOR

LIB REG

LIBOR Regime

Figure 4

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FT Returns

FT REG

FT Returns Regime

Sheet2

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GDP Growth

GDP REG

GDP Growth Regime

Sheet3

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FT Returns

FT 1

FT2


IPD ReturnsAR-TARAR

1986Q4

1987Q12.44

1987Q22.723.047.48

1987Q34.957.4742.57

1987Q45.626.3716.88

1988Q15.204.72-1.92

1988Q28.0311.2255.86

1988Q37.266.40-5.71

1988Q46.696.04-3.04

1989Q14.792.65-27.22

1989Q25.175.6011.64

1989Q34.213.12-12.10

1989Q41.28-2.02-48.11

1990Q1-0.09-1.64-23.25

1990Q2-2.36-4.91-40.63

1990Q3-2.14-1.901.45

1990Q4-2.03-1.90-0.10

1991Q1-1.68-1.284.29

1991Q2-0.091.7126.77

1991Q3-0.05-0.010.55

1991Q41.062.3219.83

1992Q10.30-0.56-12.61

1992Q20.390.481.87

1992Q3-0.82-2.17-21.13

1992Q40.051.0314.73

1993Q10.831.7113.97

1993Q22.494.3630.49

1993Q33.835.3426.47

1993Q47.9512.5977.50

1994Q17.547.080.64

1994Q23.79-0.44-59.56

1994Q31.82-0.39-31.36

1994Q41.050.18-11.98

1995Q10.910.74-1.55

1995Q20.43-0.11-7.59

1995Q30.931.509.39

1995Q40.880.830.07

1996Q11.752.7216.34

1996Q22.092.477.84

1996Q32.082.061.86

1996Q43.034.1019.11

1997Q12.952.851.56

1997Q23.444.0011.78

1997Q33.433.433.34

1997Q44.535.7623.01

1998Q13.221.75-18.83

1998Q23.744.3312.52

1998Q32.801.73-13.16

1998Q41.700.47-16.77

1999Q12.072.488.25

1999Q23.635.3930.00

1999Q33.613.593.25

1999Q43.914.248.94

2000Q13.072.13-11.01

2000Q22.561.99-6.03

2000Q32.312.02-2.00

2000Q42.051.75-2.41

2001Q11.771.47-2.81

2001Q21.671.55-0.08

2001Q31.531.36-0.91

2001Q41.852.227.37

2002Q11.881.922.38

2002Q22.853.9519.26

2002Q32.822.792.29

2002Q42.381.88-5.10

2003Q11.971.50-5.00

2003Q22.633.3813.87

2003Q32.782.945.20

2003Q43.273.8411.68

2004Q13.433.616.10

2004Q24.816.3628.07

2004Q34.243.60-5.37

2004Q44.825.4814.70

2005Q12.640.17-34.34

2005Q24.396.3834.09

2005Q34.324.243.12

2005Q45.907.6832.51

2006Q14.352.61-21.75

2006Q24.945.6114.94

2006Q33.652.20-18.16

2006Q43.703.754.48

2007Q12.230.58-22.53

2007Q22.081.91-0.49

2007Q3-1.02-4.51-53.36

2007Q4-8.93-17.84-142.46

2008Q1-3.442.7589.19

2008Q2-2.70-1.869.87

2008Q3-4.89-7.36-41.86

2008Q4-14.51-25.36-177.01

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IPD Returns

AR-TAR

AR

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IPD Returns

AR-TAR


1986Q4

1987Q12.44

1987Q22.723.457.483.85

1987Q34.9510.6742.5713.86

1987Q45.627.3316.888.29

1988Q15.20-5.34-1.923.51

1988Q28.0315.3055.8619.36

1988Q37.265.29-5.714.19

1988Q46.695.21-3.044.38

1989Q14.79-0.08-27.22-2.79

1989Q25.176.1611.646.70

1989Q34.211.73-12.100.34

1989Q41.28-6.23-48.11-10.42

1990Q1-0.09-3.61-23.25-5.57

1990Q2-2.36-8.17-40.63-11.42

1990Q3-2.14-1.601.45-1.29

1990Q4-2.030.83-0.10-1.57

1991Q1-1.68-0.774.29-0.26

1991Q2-0.094.0026.776.27

1991Q3-0.050.040.550.09

1991Q41.063.9119.835.51

1992Q10.30-1.66-12.61-2.76

1992Q20.390.611.870.74

1992Q3-0.82-3.91-21.13-5.63

1992Q40.052.2814.733.53

1993Q10.832.8313.973.94

1993Q22.496.7430.499.12

1993Q33.837.2726.479.19

1993Q47.9518.5277.5024.42

1994Q17.546.490.645.90

1994Q23.79-5.84-59.56-11.22

1994Q31.82-3.22-31.36-6.04

1994Q41.05-0.93-11.98-2.04

1995Q10.910.53-1.550.32

1995Q20.43-0.79-7.59-1.47

1995Q30.932.229.392.93

1995Q40.880.760.070.69

1996Q11.753.9716.345.20

1996Q22.092.967.843.45

1996Q32.082.041.862.02

1996Q43.035.4719.116.84

1997Q12.952.741.562.62

1997Q23.444.7111.785.42

1997Q33.433.423.343.41

1997Q44.537.3423.018.91

1998Q13.22-0.13-18.83-2.00

1998Q23.745.0812.525.82

1998Q32.800.37-13.16-0.98

1998Q41.70-25.63-16.77-2.67

1999Q12.073.018.253.53

1999Q23.637.6430.009.88

1999Q33.613.553.253.52

1999Q43.914.678.945.10

2000Q13.070.93-11.01-0.26

2000Q22.561.26-6.030.53

2000Q32.311.65-2.001.29

2000Q42.051.37-2.410.99

2001Q11.771.08-2.810.69

2001Q21.671.41-0.081.26

2001Q31.531.16-0.910.95

2001Q41.8510.027.373.16

2002Q11.881.962.382.00

2002Q22.855.3519.266.74

2002Q32.822.742.292.70

2002Q42.38-8.68-5.100.61

2003Q11.970.91-5.000.32

2003Q22.634.3413.875.29

2003Q32.783.145.203.35

2003Q43.274.5511.685.27

2004Q13.433.846.104.06

2004Q24.818.3428.0710.32

2004Q34.242.78-5.371.96

2004Q44.826.3314.707.16

2005Q12.64-2.99-34.34-6.12

2005Q24.398.9134.0911.43

2005Q34.324.143.124.04

2005Q45.909.9432.5112.20

2006Q14.350.39-21.75-1.83

2006Q24.946.4614.947.31

2006Q33.650.34-18.16-1.51

2006Q43.703.824.483.88

2007Q12.23-1.53-22.53-3.63

2007Q22.081.69-0.491.47

2007Q3-1.02-8.97-53.36-13.42

2007Q4-8.93-29.22-142.46-40.55

2008Q1-3.4410.6489.1918.50

2008Q2-2.70-0.799.870.28

2008Q3-4.89-10.50-41.86-13.64

2008Q4-14.51-39.21-177.01-53.00

2.141.25-1.151.36

3.277.9534.119.82

0.8130.1990.0980.222

-1.999-2.514-2.154-2.721

8.06510.31010.84413.726


IPD1.000

TAR TAR0.7371.000

AR AR0.6180.8891.000

Alpha 0.80.7620.9190.9801.000

2.62

-53.00

24.42

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IPD Returns

TAR-TAR

AR

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IPD Returns

TAR-TAR

alpha 0.8

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IPD Returns

TAR-TAR

TAR-TAR Model Focus on FT and LIBOR regimes All bar LIBOR-FT models improve SSE Best Model FT-FT All Coefficients Save f1 significant

Model

SSE

TAR

LIBOR-LIBOR

1.42**

(0.28)

0.73**

(0.07)

-0.37

(1.33)

0.79**

(0.14)

3.05**

(0.68)

-0.04

(0.15)

6.21

11.31

0.55

0.00

0.33

0.12

250.3

FT-FT

0.72**

(0.07)

0.96**

(0.04)

3.36**

(0.70)

0.01

(0.09)

-7.13*

(2.61)

1.40**

(0.41)

-13.33

-1.20

0.07

0.00

0.19

0.74

183.2

LIBOR-FT

1.40**

(0.24)

0.56**

(0.09)

1.63**

(0.61)

0.35**

(0.12)

5.28**

(1.61)

-0.85*

(0.42)

6.21

-1.79

0.15

0.40

0.09

0.36

335.9

FT-LIBOR

0.79**

(0.10)

2.22**

(0.80)

0.24

(1.49)

0.59*

(0.29)

3.34**

(1.03)

-0.18

(0.13)

-13.34

5.95

0.02

0.06

0.41

0.51

211.8

AR

0.94**

(0.04)

-1.35

(2.82)

0.12

(0.15)

309.5

_1335081039.unknown

_1335081043.unknown

_1335081045.unknown

_1335081046.unknown

_1335081047.unknown

_1335081044.unknown

_1335081041.unknown

_1335081042.unknown

_1335081040.unknown

_1335081037.unknown

_1335081038.unknown

_1335081036.unknown

TAR-TAR (FT Model)Return Processes Differ:FT Returns > -1.2% steady growthFT Returns < -1.2% negative, explosive autoreg.Implies very sharply falling underlying returnsLow regime occurs 26% of timeRegime not persistent Smoothing Processes Differ:FT Returns < -13% very strong smoothingInformation story? This state occurs 7% of time Smoothing parameter lower in other regime

TAR-TAR: FT RegimesReturns Regime: C1 = -1.2%Smoothing Regime: C2 = -13.2%

Chart7

18.841917038-13.33-1.2

15.2607927322-13.33-1.2

5.616584-13.33-1.2

-32.0026550293-13.33-1.2

4.0549674034-13.33-1.2

8.310058-13.33-1.2

-0.4158257-13.33-1.2

-1.0190192461-13.33-1.2

15.8391513824-13.33-1.2

3.7536697388-13.33-1.2

7.152185-13.33-1.2

4.0634436607-13.33-1.2

-6.530186-13.33-1.2

6.268623-13.33-1.2

-18.13032341-13.33-1.2

8.147772-13.33-1.2

15.4552135468-13.33-1.2

-1.2575266361-13.33-1.2

10.16984272-13.33-1.2

-5.514645-13.33-1.2

-0.1393856108-13.33-1.2

5.096318-13.33-1.2

0.4986844361-13.33-1.2

13.169506073-13.33-1.2

4.48695-13.33-1.2

2.6163947582-13.33-1.2

6.1890354156-13.33-1.2

11.74033-13.33-1.2

-6.432471-13.33-1.2

-5.54714-13.33-1.2

4.34841-13.33-1.2

1.5851967335-13.33-1.2

2.368151-13.33-1.2

6.381937-13.33-1.2

7.720172-13.33-1.2

4.887479-13.33-1.2

3.473517-13.33-1.2

1.800711-13.33-1.2

5.992757-13.33-1.2

4.1683225632-13.33-1.2

5.147196-13.33-1.2

5.052799-13.33-1.2

12.3165931702-13.33-1.2

-1.3730785847-13.33-1.2

15.0943746567-13.33-1.2

-0.798896-13.33-1.2

-14.9692277908-13.33-1.2

13.5682315826-13.33-1.2

8.746055-13.33-1.2

2.3110244274-13.33-1.2

-3.4791407585-13.33-1.2

14.09605-13.33-1.2

-3.4921572208-13.33-1.2

-2.1302621365-13.33-1.2

0.6456831-13.33-1.2

-1.105868-13.33-1.2

-8.800473-13.33-1.2

1.1919534206-13.33-1.2

-14.55667-13.33-1.2

7.903409481-13.33-1.2

2.2446427345-13.33-1.2

-11.5977525711-13.33-1.2

-21.8640575409-13.33-1.2

4.577512-13.33-1.2

-6.516522-13.33-1.2

13.5642137527-13.33-1.2

3.8169956207-13.33-1.2

8.995739-13.33-1.2

0.6180823445-13.33-1.2

2.171329-13.33-1.2

2.8292126656-13.33-1.2

6.4608635902-13.33-1.2

3.003842-13.33-1.2

4.8901615143-13.33-1.2

7.847241-13.33-1.2

4.178603-13.33-1.2

7.783821-13.33-1.2

-1.8546527624-13.33-1.2

3.5838816166-13.33-1.2

5.97447-13.33-1.2

2.865909338-13.33-1.2

4.441267-13.33-1.2

-1.7781077623-13.33-1.2

-0.3495439-13.33-1.2

-10.37297-13.33-1.2

-1.4569555521-13.33-1.2

-12.993262291-13.33-1.2

-10.742609024-13.33-1.2

FT Returns

FT 1

FT2


Figure 1 & 3


1986Q411.251.706.25-1.54-0.41-13.33-1.2LIBOR6.25FT1-13.33

1987Q12.442.4410.0018.840.506.25-1.54-0.41-13.33-1.2FT-1.54FT2-1.2

1987Q22.722.729.2515.261.106.25-1.54-0.41-13.33-1.2GDP-0.41

1987Q34.954.9510.385.622.206.25-1.54-0.41-13.33-1.2

1987Q45.625.628.94-32.000.906.25-1.54-0.41-13.33-1.2

1988Q15.205.208.694.051.706.25-1.54-0.41-13.33-1.2

1988Q28.038.039.888.310.506.25-1.54-0.41-13.33-1.2

1988Q37.267.2611.94-0.421.406.25-1.54-0.41-13.33-1.2

1988Q46.696.6913.25-1.020.706.25-1.54-0.41-13.33-1.2

1989Q14.794.7913.0615.840.406.25-1.54-0.41-13.33-1.2

1989Q25.175.1714.253.750.606.25-1.54-0.41-13.33-1.2

1989Q34.214.2114.697.150.106.25-1.54-0.41-13.33-1.2

1989Q41.281.2815.164.060.106.25-1.54-0.41-13.33-1.2

1990Q1-0.09-0.0915.25-6.530.806.25-1.54-0.41-13.33-1.2

1990Q2-2.36-2.3614.976.270.506.25-1.54-0.41-13.33-1.2

1990Q3-2.14-2.1414.97-18.13-1.206.25-1.54-0.41-13.33-1.2

1990Q4-2.03-2.0314.068.15-0.606.25-1.54-0.41-13.33-1.2

1991Q1-1.68-1.6812.4415.46-0.106.25-1.54-0.41-13.33-1.2

1991Q2-0.09-0.0911.31-1.26-0.306.25-1.54-0.41-13.33-1.2

1991Q3-0.05-0.0510.3410.17-0.406.25-1.54-0.41-13.33-1.2

1991Q41.061.0610.94-5.510.106.25-1.54-0.41-13.33-1.2

1992Q10.300.3010.81-0.140.106.25-1.54-0.41-13.33-1.2

1992Q20.390.3910.135.10-0.206.25-1.54-0.41-13.33-1.2

1992Q3

Documents

Unsmoothing Real Estate Returns: A Regime Switching Approach Colin Lizieri, Stephen Satchell and Warapong Wonwachara Department of Land Economy / Department