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Investment in “Real Time” and“High Definition”: A Big Data Approach
November 2020
2020 Conference on Nontraditional Data & Statistical LearningBanca d’ Italia and Federal Reserve Board
Ali.B. Barlas, Seda Güler, Alvaro Ortiz & Tomasa Rodrigo
2Investment in ”Real Time” & ”High Definition”: A Big Data approach
The Covid-19 crisis has reinforced the potential of Big Data tools forEconomic Analysis and Policymaking
The high uncertainty triggered by the Covid-19 crisis has stressed the need to monitor the evolution ofthe economy in “real time”. These efforts have been materialized in several ways:
- Focusing on timely, alternative indicators: soft data surveys (particularly the PurchasingManager Indexes, PMIs) and other high frequency indicators like electricity production or chain
store sales released on daily or weekly basis.
- Developing higher frequency models: Some CBs have relied on this High Frequency indicatorsto develop weekly activity tracker models such as the FED´WEI (Lewis, 2020) and the
Bundesbank WAI (Eraslan, S. and T. Götz, 2020).
- Developing New Big Data Indicators*: Focusing on daily aggregate information of bankingtransactions to track consumption, employment , turnover, mobility (link to our BigData Project).
* Some of the Recent literature on Big Data analysis Andersen, Hansen, Johannesen, & Sheridan (2020a), Andersen, Hansen, Johannesen, & Sheridan (2020b), Alexander & Karger (2020), Baker, Farrokhnia, Meyer, Pagel, & Yannelis (2020a), Baker, Farrokhnia, Meyer, Pagel, & Yannelis (2020b), Bounie, Camara, & Galbraith (2020), Chetty, Friedman, Hendren, & Stepner (2020), Chronopoulos, Lukas, & Wilson (2020), Cox, Ganong, Noel, Vavra, Wong, Farrell, & Greig (2020), Surico, Kanzig, & Hacioglu (2020).
3Investment in ”Real Time” & ”High Definition”: A Big Data approach
Through the analysis of the firm-to-firm transactions we extend ourproject of national accounts in real time & high definition to Investment
The investment spending is done mostly by companies and, to a lesser extent, by individualsWe track investment payments through
Firms are classified by their NACE codes to identify their business activity (in line with the European statistical classification of sectors)
firm to firm transactionsindividual to firm transactions
Construction Investment
We approximate investment demand in one type of asset taking into account the aggregate flows or transactions done from any firm or individual to the sector which produce the fixed assets
Machinery Investment*Total Investment*Machinery & Equipment, Media & ICT, Agriculture & Animals, Forestry, Durable Goods, Retail Trade, Textile & Clothing, Transportation and Shipping.
4Investment in ”Real Time” & ”High Definition”: A Big Data approach
The case of Turkey: Data and Representativeness
5Investment in ”Real Time” & ”High Definition”: A Big Data approach
Validation I: The Big Data investment index shows a high correlationand co-movement with the oficial data TURKEY: GBBBVA BIG DATA INVESTMENT INDICES (28-day cum. YoY real )
Correlation coefficient: 0.88
Total Investment
Correlation coefficient: 0.84 Correlation coefficient: 0.77
Maquinery & Equipment Construction
Source: Own Calculations
6Investment in ”Real Time” & ”High Definition”: A Big Data approach
Validation II: The sincrony of BigData Investment with the Investment
Cycle is validated by the high correlation coefficients with HF proxies
-40%
-30%
-20%
-10%
0%
10%
20%
30%
40%
-50%
-40%
-30%
-20%
-10%
0%
10%
20%
30%
Sep
-17
No
v-1
7Ja
n-1
8M
ar-
18M
ay-
18
Jul-1
8S
ep-1
8N
ov-
18
Jan-
19
Ma
r-19
Ma
y-1
9Ju
l-19
Sep
-19
No
v-1
9Ja
n-2
0M
ar-
20M
ay-
20
Jul-2
0S
ep-2
0N
ov-
20
Garanti BBVA Big Data Construction Index 3mEmployment in ConstructionNon-Metalic Mineral (Cement)Turnover Building - rhs
BBVA BIG DATA INVESTMENT & HIGH FREQUENCY PROXIES (28-day cum. YoY real )
Maquinery & Equipment ConstructionCorrelation coefficient: 0.75
Correlation coefficient: 0.79
Correlation coefficient: 0.85
Correlation coefficient: 0.72
Correlation coefficient: 0.90
Source: Own Calculation
7Investment in ”Real Time” & ”High Definition”: A Big Data approach
Investment Big Data in an Nowcasting Model (DFM): The framework
9ECB
Working Paper Series No 1189May 2010
the forecast accuracy of these specifications with that of univariate benchmarks as well as of the model ofBanbura and Runstler (2010), who adopt the methodology of Giannone, Reichlin, and Small (2008) to thecase of euro area.
Giannone, Reichlin, and Small (2008) have proposed a factor model framework, which allows to deal with“ragged edge” and exploit information from large data sets in a timely manner. They have applied it tonowcasting of US GDP from a large number of monthly indicators. While Giannone, Reichlin, and Small(2008) can handle the “ragged edge” problem, it is not straightforward to apply their methodology tomixed frequency panels with series of different lengths or, in general, to any pattern of missing data.8 Inaddition, as the estimation is based on principal components, it could be inefficient for small samples.
Other papers related to ours include Camacho and Perez-Quiros (2008) who obtain real-time estimates ofthe euro area GDP from monthly indicators from a small scale model applying the mixed frequency factormodel approach of Mariano and Murasawa (2003). Schumacher and Breitung (2008) forecast German GDPfrom large number of monthly indicators using the EM approach proposed by Stock and Watson (2002b).
and shows how to incorporate relevant accounting and temporary constraints. Angelini, Henry, andMarcellino (2006) propose methodology for backdating and interpolation based on large cross-sections. Incontrast to theirs, our method exploits the dynamics of the data and is based on maximum likelihoodwhich allows for imposing restrictions and is more efficient for smaller cross-sections.
The paper is organized as follows. Section 2 presents the model, discusses the estimation and explains howthe news content can be extracted. Section 3 provides the results of the Monte Carlo experiment. Section4 describes the empirical application. Section 5 concludes. The technical details and data description areprovided in the Appendix.
2 Econometric framework
Let yt = [y1,t, y2,t, . . . , yn,t]′ , t = 1, . . . , T denote a stationary n-dimensional vector process standardised
to mean 0 and unit variance. We assume that yt admits the following factor model representation:
yt = Λft + εt , (1)
where ft is a r× 19 vector of (unobserved) common factors and εt = [ε1,t, ε2,t, . . . , εn,t]′ is the idiosyncratic
component, uncorrelated with ft at all leads and lags. The n×r matrix Λ contains factor loadings. χt = Λft
is referred to as the common component. It is assumed that εt is normally distributed and cross-sectionallyuncorrelated, i.e. yt follows an exact factor model. We also shortly discuss validity of the approach inthe case of an approximate factor model, see below. What concerns the dynamics of the idiosyncraticcomponent we consider two cases: εt is serially uncorrelated or it follows an AR(1) process.
Further, it is assumed that the common factors ft follow a stationary VAR process of order p:
ft = A1ft−1 + A2ft−2 + · · · + Apft−p + ut , ut ∼ i.i.d. N (0, Q) , (2)
where A1, . . . , Ap are r×r matrices of autoregressive coefficients. We collect the latter into A = [A1, . . . , Ap].8Their estimation approach consists of two steps. First, the parameters of the state space representation of the factor
model are obtained using a principal components based procedure applied to a truncated data set (without missing data).Second, Kalman filter is applied on the full data set in order to obtain factor estimates and forecasts using all availableinformation.
9For identification it is required that 2r + 1 ≤ n, see e.g. Geweke and Singleton (1980).
Proietti (2008) estimates a factor model for interpolation of GDP and itsmain components
9
ECBWorking Paper Series No 1189
May 2010
the forecast accuracy of these specifications with that of univariate benchmarks as well as of the model ofBanbura and Runstler (2010), who adopt the methodology of Giannone, Reichlin, and Small (2008) to thecase of euro area.
Giannone, Reichlin, and Small (2008) have proposed a factor model framework, which allows to deal with“ragged edge” and exploit information from large data sets in a timely manner. They have applied it tonowcasting of US GDP from a large number of monthly indicators. While Giannone, Reichlin, and Small(2008) can handle the “ragged edge” problem, it is not straightforward to apply their methodology tomixed frequency panels with series of different lengths or, in general, to any pattern of missing data.8 Inaddition, as the estimation is based on principal components, it could be inefficient for small samples.
Other papers related to ours include Camacho and Perez-Quiros (2008) who obtain real-time estimates ofthe euro area GDP from monthly indicators from a small scale model applying the mixed frequency factormodel approach of Mariano and Murasawa (2003). Schumacher and Breitung (2008) forecast German GDPfrom large number of monthly indicators using the EM approach proposed by Stock and Watson (2002b).
and shows how to incorporate relevant accounting and temporary constraints. Angelini, Henry, andMarcellino (2006) propose methodology for backdating and interpolation based on large cross-sections. Incontrast to theirs, our method exploits the dynamics of the data and is based on maximum likelihoodwhich allows for imposing restrictions and is more efficient for smaller cross-sections.
The paper is organized as follows. Section 2 presents the model, discusses the estimation and explains howthe news content can be extracted. Section 3 provides the results of the Monte Carlo experiment. Section4 describes the empirical application. Section 5 concludes. The technical details and data description areprovided in the Appendix.
2 Econometric framework
Let yt = [y1,t, y2,t, . . . , yn,t]′ , t = 1, . . . , T denote a stationary n-dimensional vector process standardised
to mean 0 and unit variance. We assume that yt admits the following factor model representation:
yt = Λft + εt , (1)
where ft is a r× 19 vector of (unobserved) common factors and εt = [ε1,t, ε2,t, . . . , εn,t]′ is the idiosyncratic
component, uncorrelated with ft at all leads and lags. The n×r matrix Λ contains factor loadings. χt = Λft
is referred to as the common component. It is assumed that εt is normally distributed and cross-sectionallyuncorrelated, i.e. yt follows an exact factor model. We also shortly discuss validity of the approach inthe case of an approximate factor model, see below. What concerns the dynamics of the idiosyncraticcomponent we consider two cases: εt is serially uncorrelated or it follows an AR(1) process.
Further, it is assumed that the common factors ft follow a stationary VAR process of order p:
ft = A1ft−1 + A2ft−2 + · · · + Apft−p + ut , ut ∼ i.i.d. N (0, Q) , (2)
where A1, . . . , Ap are r×r matrices of autoregressive coefficients. We collect the latter into A = [A1, . . . , Ap].8Their estimation approach consists of two steps. First, the parameters of the state space representation of the factor
model are obtained using a principal components based procedure applied to a truncated data set (without missing data).Second, Kalman filter is applied on the full data set in order to obtain factor estimates and forecasts using all availableinformation.
9For identification it is required that 2r + 1 ≤ n, see e.g. Geweke and Singleton (1980).
Proietti (2008) estimates a factor model for interpolation of GDP and itsmain components
10
ECBWorking Paper Series No 1189May 2010
2.1 Estimation
As ft are unobserved, the maximum likelihood estimators of the parameters of model (1)-(2), which wecollect in θ, are in general not available in closed form. On the other hand, a direct numerical maximisationof the likelihood is computationally demanding, in particular for large n due to the large number ofparameters.10
In this paper we adopt an approach based on the Expectation-Maximisation (EM) algorithm, which wasproposed by Dempster, Laird, and Rubin (1977) as a general solution to problems for which incomplete orlatent data yield the likelihood intractable or difficult to deal with. The essential idea of the algorithm isto write the likelihood as if the data were complete and to iterate between two steps: in the Expectationstep we “fill in” the missing data in the likelihood, while in the Maximisation step we re-optimise thisexpectation. Under some regularity conditions, the EM algorithm converges towards a local maximum ofthe likelihood (or a point in its ridge, see also below).
To derive the EM steps for the model described above, let us denote the joint log-likelihood of yt andft, t = 1, . . . , T by l(Y, F ; θ), where Y = [y1, . . . , yT ] and F = [f1, . . . , fT ]. Given the available dataΩT ⊆ Y ,11 EM algorithm proceeds in a sequence of two alternating steps:
1. E-step - the expectation of the log-likelihood conditional on the data is calculated using the estimatesfrom the previous iteration, θ(j):
L(θ, θ(j)) = Eθ(j)
[l(Y, F ; θ)|ΩT
];
2. M-step - the parameters are re-estimated through the maximisation of the expected log-likelihoodwith respect to θ:
θ(j + 1) = arg maxθ
L(θ, θ(j)) . (3)
Watson and Engle (1983) and Shumway and Stoffer (1982) show how to derive the maximisation step (3)for models similar to the one given by (1)-(2). As a result the estimation problem is reduced to a sequenceof simple steps, each of which essentially involves a pass of the Kalman smoother and two multivariateregressions. Doz, Giannone, and Reichlin (2006) show that the EM algorithm is a valid approach for themaximum likelihood estimation of factor models for large cross-sections as it is robust, easy to implementand computationally inexpensive. Watson and Engle (1983) assume that all the observations in yt areavailable (ΩT = Y ). Shumway and Stoffer (1982) derive the modifications for the missing data case butonly with known Λ. We provide the EM steps for the general case with missing data.
In the main text, we set for simplicity p = 1 (A = A1), the case of p > 1 is discussed in the Appendix. Wefirst consider the case of serially uncorrelated εt:
εt ∼ i.i.d. N (0, R) , (4)
where R is a diagonal matrix. In that case θ = Λ, A,R,Q and the maximisation of (3) results in the10Recently, Jungbacker and Koopman (2008) have shown how to reduce the computational complexity related to estimation
and smoothing if the number of observables is much larger than the number of factors.11ΩT ⊆ Y because some observations in yt can be missing.
10ECBWorking Paper Series No 1189May 2010
2.1 Estimation
As ft are unobserved, the maximum likelihood estimators of the parameters of model (1)-(2), which wecollect in θ, are in general not available in closed form. On the other hand, a direct numerical maximisationof the likelihood is computationally demanding, in particular for large n due to the large number ofparameters.10
In this paper we adopt an approach based on the Expectation-Maximisation (EM) algorithm, which wasproposed by Dempster, Laird, and Rubin (1977) as a general solution to problems for which incomplete orlatent data yield the likelihood intractable or difficult to deal with. The essential idea of the algorithm isto write the likelihood as if the data were complete and to iterate between two steps: in the Expectationstep we “fill in” the missing data in the likelihood, while in the Maximisation step we re-optimise thisexpectation. Under some regularity conditions, the EM algorithm converges towards a local maximum ofthe likelihood (or a point in its ridge, see also below).
To derive the EM steps for the model described above, let us denote the joint log-likelihood of yt andft, t = 1, . . . , T by l(Y, F ; θ), where Y = [y1, . . . , yT ] and F = [f1, . . . , fT ]. Given the available dataΩT ⊆ Y ,11 EM algorithm proceeds in a sequence of two alternating steps:
1. E-step - the expectation of the log-likelihood conditional on the data is calculated using the estimatesfrom the previous iteration, θ(j):
L(θ, θ(j)) = Eθ(j)
[l(Y, F ; θ)|ΩT
];
2. M-step - the parameters are re-estimated through the maximisation of the expected log-likelihoodwith respect to θ:
θ(j + 1) = arg maxθ
L(θ, θ(j)) . (3)
Watson and Engle (1983) and Shumway and Stoffer (1982) show how to derive the maximisation step (3)for models similar to the one given by (1)-(2). As a result the estimation problem is reduced to a sequenceof simple steps, each of which essentially involves a pass of the Kalman smoother and two multivariateregressions. Doz, Giannone, and Reichlin (2006) show that the EM algorithm is a valid approach for themaximum likelihood estimation of factor models for large cross-sections as it is robust, easy to implementand computationally inexpensive. Watson and Engle (1983) assume that all the observations in yt areavailable (ΩT = Y ). Shumway and Stoffer (1982) derive the modifications for the missing data case butonly with known Λ. We provide the EM steps for the general case with missing data.
In the main text, we set for simplicity p = 1 (A = A1), the case of p > 1 is discussed in the Appendix. Wefirst consider the case of serially uncorrelated εt:
εt ∼ i.i.d. N (0, R) , (4)
where R is a diagonal matrix. In that case θ = Λ, A, R, Q and the maximisation of (3) results in the10Recently, Jungbacker and Koopman (2008) have shown how to reduce the computational complexity related to estimation
and smoothing if the number of observables is much larger than the number of factors.11ΩT ⊆ Y because some observations in yt can be missing.
ExpectationMaximization (EM)
Algorithm
9ECB
Working Paper Series No 1189May 2010
the forecast accuracy of these specifications with that of univariate benchmarks as well as of the model ofBanbura and Runstler (2010), who adopt the methodology of Giannone, Reichlin, and Small (2008) to thecase of euro area.
Giannone, Reichlin, and Small (2008) have proposed a factor model framework, which allows to deal with“ragged edge” and exploit information from large data sets in a timely manner. They have applied it tonowcasting of US GDP from a large number of monthly indicators. While Giannone, Reichlin, and Small(2008) can handle the “ragged edge” problem, it is not straightforward to apply their methodology tomixed frequency panels with series of different lengths or, in general, to any pattern of missing data.8 Inaddition, as the estimation is based on principal components, it could be inefficient for small samples.
Other papers related to ours include Camacho and Perez-Quiros (2008) who obtain real-time estimates ofthe euro area GDP from monthly indicators from a small scale model applying the mixed frequency factormodel approach of Mariano and Murasawa (2003). Schumacher and Breitung (2008) forecast German GDPfrom large number of monthly indicators using the EM approach proposed by Stock and Watson (2002b).
and shows how to incorporate relevant accounting and temporary constraints. Angelini, Henry, andMarcellino (2006) propose methodology for backdating and interpolation based on large cross-sections. Incontrast to theirs, our method exploits the dynamics of the data and is based on maximum likelihoodwhich allows for imposing restrictions and is more efficient for smaller cross-sections.
The paper is organized as follows. Section 2 presents the model, discusses the estimation and explains howthe news content can be extracted. Section 3 provides the results of the Monte Carlo experiment. Section4 describes the empirical application. Section 5 concludes. The technical details and data description areprovided in the Appendix.
2 Econometric framework
Let yt = [y1,t, y2,t, . . . , yn,t]′ , t = 1, . . . , T denote a stationary n-dimensional vector process standardised
to mean 0 and unit variance. We assume that yt admits the following factor model representation:
yt = Λft + εt , (1)
where ft is a r× 19 vector of (unobserved) common factors and εt = [ε1,t, ε2,t, . . . , εn,t]′ is the idiosyncratic
component, uncorrelated with ft at all leads and lags. The n×r matrix Λ contains factor loadings. χt = Λft
is referred to as the common component. It is assumed that εt is normally distributed and cross-sectionallyuncorrelated, i.e. yt follows an exact factor model. We also shortly discuss validity of the approach inthe case of an approximate factor model, see below. What concerns the dynamics of the idiosyncraticcomponent we consider two cases: εt is serially uncorrelated or it follows an AR(1) process.
Further, it is assumed that the common factors ft follow a stationary VAR process of order p:
ft = A1ft−1 + A2ft−2 + · · · + Apft−p + ut , ut ∼ i.i.d. N (0, Q) , (2)
where A1, . . . , Ap are r×r matrices of autoregressive coefficients. We collect the latter into A = [A1, . . . , Ap].8Their estimation approach consists of two steps. First, the parameters of the state space representation of the factor
model are obtained using a principal components based procedure applied to a truncated data set (without missing data).Second, Kalman filter is applied on the full data set in order to obtain factor estimates and forecasts using all availableinformation.
9For identification it is required that 2r + 1 ≤ n, see e.g. Geweke and Singleton (1980).
Proietti (2008) estimates a factor model for interpolation of GDP and itsmain components
NowcastingAccuracy
NowcastingAnticipation
11ECB
Working Paper Series No 1189May 2010
following expressions for Λ(j + 1) and A(j + 1):12
Λ(j + 1) =
(T∑
t=1
Eθ(j)
[ytf
′t |ΩT
])(
T∑
t=1
Eθ(j)
[ftf
′t |ΩT
])−1
, (5)
A(j + 1) =
(T∑
t=1
Eθ(j)
[ftf
′t−1|ΩT
])(
T∑
t=1
Eθ(j)
[ft−1f
′t−1|ΩT
])−1
. (6)
Note that these expressions resemble the ordinary least squares solution to the maximum likelihood estima-tion for (auto-) regressions with complete data with the difference that the sufficient statistics are replacedby their expectations.
The (j + 1)-iteration covariance matrices are computed as the expectations of sums of squared residualsconditional on the updated estimates of Λ and A:13
R(j + 1) = diag
(1T
T∑
t=1
Eθ(j)
[(yt − Λ(j + 1)ft
)(yt − Λ(j + 1)ft
)′|ΩT
])(7)
= diag
(1T
(T∑
t=1
Eθ(j)
[yty
′t|ΩT
]− Λ(j + 1)
T∑
t=1
Eθ(j)
[fty
′t|ΩT
]))
and
Q(j + 1) =1T
(T∑
t=1
Eθ(j)
[ftf
′t |ΩT
]− A(j + 1)
T∑
t=1
Eθ(j)
[ft−1f
′t |ΩT
])
. (8)
When yt does not contain missing data, we have that
Eθ(j) [yty′t|ΩT ] = yty
′t and Eθ(j) [ytf
′t |ΩT ] = ytEθ(j) [f ′
t |ΩT ] . (9)
Finally, the conditional moments of the latent factors, Eθ(j) [ft|ΩT ], Eθ(j) [ftf ′t |ΩT ], Eθ(j)
[ft−1f ′
t−1|ΩT
]
and Eθ(j)
[ftf ′
t−1|ΩT
], can be obtained through the Kalman smoother for the state space representation:
yt = Λ(j)ft + εt , εt ∼ i.i.d. N (0, R(j)) ,
ft = A(j)ft−1 + ut , ut ∼ i.i.d. N (0, Q(j)) , (10)
see Watson and Engle (1983).
However, when yt contains missing values we can no longer use (9) when developing the expressions (5)and (7). Let Wt be a diagonal matrix of size n with ith diagonal element equal to 0 if yi,t is missing andequal to 1 otherwise. As shown in the Appendix, Λ(j + 1) can be obtained as
vec(Λ(j + 1)
)=
(T∑
t=1
Eθ(j)
[ftf
′t |ΩT
]⊗ Wt
)−1
vec
(T∑
t=1
WtytEθ(j)
[f ′
t |ΩT
])
. (11)
Intuitively, Wt works as a selection matrix, so that only the available data are used in the calculations.Analogously, the expression (7) becomes
R(j + 1) = diag
(1T
T∑
t=1
(Wtyty
′tW
′t − WtytEθ(j)
[f ′
t |ΩT
]Λ(j + 1)′Wt − WtΛ(j + 1)Eθ(j)
[ft|ΩT
]y′
tWt
+ WtΛ(j + 1)Eθ(j)
[ftf
′t |ΩT
]Λ(j + 1)′Wt + (I − Wt)R(j)(I − Wt)
)). (12)
12A sketch of how these are derived is provided in the Appendix, see also e.g. Watson and Engle (1983) and Shumway andStoffer (1982).
13Note that L(θ, θ(j)) does not have to be maximised simultaneously with respect to all the parameters. The procedureremains valid if M-step is performed sequentially, i.e. L(θ, θ(j)) is maximised over a subvector of θ with other parametersheld fixed at their current values, see e.g. McLachlan and Krishnan (1996), Ch. 5.
A Dynamic factor Model(DFM)
11ECB
Working Paper Series No 1189May 2010
following expressions for Λ(j + 1) and A(j + 1):12
Λ(j + 1) =
(T∑
t=1
Eθ(j)
[ytf
′t |ΩT
])(
T∑
t=1
Eθ(j)
[ftf
′t |ΩT
])−1
, (5)
A(j + 1) =
(T∑
t=1
Eθ(j)
[ftf
′t−1|ΩT
])(
T∑
t=1
Eθ(j)
[ft−1f
′t−1|ΩT
])−1
. (6)
Note that these expressions resemble the ordinary least squares solution to the maximum likelihood estima-tion for (auto-) regressions with complete data with the difference that the sufficient statistics are replacedby their expectations.
The (j + 1)-iteration covariance matrices are computed as the expectations of sums of squared residualsconditional on the updated estimates of Λ and A:13
R(j + 1) = diag
(1T
T∑
t=1
Eθ(j)
[(yt − Λ(j + 1)ft
)(yt − Λ(j + 1)ft
)′|ΩT
])(7)
= diag
(1T
(T∑
t=1
Eθ(j)
[yty
′t|ΩT
]− Λ(j + 1)
T∑
t=1
Eθ(j)
[fty
′t|ΩT
]))
and
Q(j + 1) =1T
(T∑
t=1
Eθ(j)
[ftf
′t |ΩT
]− A(j + 1)
T∑
t=1
Eθ(j)
[ft−1f
′t |ΩT
])
. (8)
When yt does not contain missing data, we have that
Eθ(j) [yty′t|ΩT ] = yty
′t and Eθ(j) [ytf
′t |ΩT ] = ytEθ(j) [f ′
t |ΩT ] . (9)
Finally, the conditional moments of the latent factors, Eθ(j) [ft|ΩT ], Eθ(j) [ftf ′t |ΩT ], Eθ(j)
[ft−1f ′
t−1|ΩT
]
and Eθ(j)
[ftf ′
t−1|ΩT
], can be obtained through the Kalman smoother for the state space representation:
yt = Λ(j)ft + εt , εt ∼ i.i.d. N (0, R(j)) ,
ft = A(j)ft−1 + ut , ut ∼ i.i.d. N (0, Q(j)) , (10)
see Watson and Engle (1983).
However, when yt contains missing values we can no longer use (9) when developing the expressions (5)and (7). Let Wt be a diagonal matrix of size n with ith diagonal element equal to 0 if yi,t is missing andequal to 1 otherwise. As shown in the Appendix, Λ(j + 1) can be obtained as
vec(Λ(j + 1)
)=
(T∑
t=1
Eθ(j)
[ftf
′t |ΩT
]⊗ Wt
)−1
vec
(T∑
t=1
WtytEθ(j)
[f ′
t |ΩT
])
. (11)
Intuitively, Wt works as a selection matrix, so that only the available data are used in the calculations.Analogously, the expression (7) becomes
R(j + 1) = diag
(1T
T∑
t=1
(Wtyty
′tW
′t − WtytEθ(j)
[f ′
t |ΩT
]Λ(j + 1)′Wt − WtΛ(j + 1)Eθ(j)
[ft|ΩT
]y′
tWt
+ WtΛ(j + 1)Eθ(j)
[ftf
′t |ΩT
]Λ(j + 1)′Wt + (I − Wt)R(j)(I − Wt)
)). (12)
12A sketch of how these are derived is provided in the Appendix, see also e.g. Watson and Engle (1983) and Shumway andStoffer (1982).
13Note that L(θ, θ(j)) does not have to be maximised simultaneously with respect to all the parameters. The procedureremains valid if M-step is performed sequentially, i.e. L(θ, θ(j)) is maximised over a subvector of θ with other parametersheld fixed at their current values, see e.g. McLachlan and Krishnan (1996), Ch. 5.
11ECB
Working Paper Series No 1189May 2010
following expressions for Λ(j + 1) and A(j + 1):12
Λ(j + 1) =
(T∑
t=1
Eθ(j)
[ytf
′t |ΩT
])(
T∑
t=1
Eθ(j)
[ftf
′t |ΩT
])−1
, (5)
A(j + 1) =
(T∑
t=1
Eθ(j)
[ftf
′t−1|ΩT
])(
T∑
t=1
Eθ(j)
[ft−1f
′t−1|ΩT
])−1
. (6)
Note that these expressions resemble the ordinary least squares solution to the maximum likelihood estima-tion for (auto-) regressions with complete data with the difference that the sufficient statistics are replacedby their expectations.
The (j + 1)-iteration covariance matrices are computed as the expectations of sums of squared residualsconditional on the updated estimates of Λ and A:13
R(j + 1) = diag
(1T
T∑
t=1
Eθ(j)
[(yt − Λ(j + 1)ft
)(yt − Λ(j + 1)ft
)′|ΩT
])(7)
= diag
(1T
(T∑
t=1
Eθ(j)
[yty
′t|ΩT
]− Λ(j + 1)
T∑
t=1
Eθ(j)
[fty
′t|ΩT
]))
and
Q(j + 1) =1T
(T∑
t=1
Eθ(j)
[ftf
′t |ΩT
]− A(j + 1)
T∑
t=1
Eθ(j)
[ft−1f
′t |ΩT
])
. (8)
When yt does not contain missing data, we have that
Eθ(j) [yty′t|ΩT ] = yty
′t and Eθ(j) [ytf
′t |ΩT ] = ytEθ(j) [f ′
t |ΩT ] . (9)
Finally, the conditional moments of the latent factors, Eθ(j) [ft|ΩT ], Eθ(j) [ftf ′t |ΩT ], Eθ(j)
[ft−1f ′
t−1|ΩT
]
and Eθ(j)
[ftf ′
t−1|ΩT
], can be obtained through the Kalman smoother for the state space representation:
yt = Λ(j)ft + εt , εt ∼ i.i.d. N (0, R(j)) ,
ft = A(j)ft−1 + ut , ut ∼ i.i.d. N (0, Q(j)) , (10)
see Watson and Engle (1983).
However, when yt contains missing values we can no longer use (9) when developing the expressions (5)and (7). Let Wt be a diagonal matrix of size n with ith diagonal element equal to 0 if yi,t is missing andequal to 1 otherwise. As shown in the Appendix, Λ(j + 1) can be obtained as
vec(Λ(j + 1)
)=
(T∑
t=1
Eθ(j)
[ftf
′t |ΩT
]⊗ Wt
)−1
vec
(T∑
t=1
WtytEθ(j)
[f ′
t |ΩT
])
. (11)
Intuitively, Wt works as a selection matrix, so that only the available data are used in the calculations.Analogously, the expression (7) becomes
R(j + 1) = diag
(1T
T∑
t=1
(Wtyty
′tW
′t − WtytEθ(j)
[f ′
t |ΩT
]Λ(j + 1)′Wt − WtΛ(j + 1)Eθ(j)
[ft|ΩT
]y′
tWt
+ WtΛ(j + 1)Eθ(j)
[ftf
′t |ΩT
]Λ(j + 1)′Wt + (I − Wt)R(j)(I − Wt)
)). (12)
12A sketch of how these are derived is provided in the Appendix, see also e.g. Watson and Engle (1983) and Shumway andStoffer (1982).
13Note that L(θ, θ(j)) does not have to be maximised simultaneously with respect to all the parameters. The procedureremains valid if M-step is performed sequentially, i.e. L(θ, θ(j)) is maximised over a subvector of θ with other parametersheld fixed at their current values, see e.g. McLachlan and Krishnan (1996), Ch. 5.
11ECB
Working Paper Series No 1189May 2010
following expressions for Λ(j + 1) and A(j + 1):12
Λ(j + 1) =
(T∑
t=1
Eθ(j)
[ytf
′t |ΩT
])(
T∑
t=1
Eθ(j)
[ftf
′t |ΩT
])−1
, (5)
A(j + 1) =
(T∑
t=1
Eθ(j)
[ftf
′t−1|ΩT
])(
T∑
t=1
Eθ(j)
[ft−1f
′t−1|ΩT
])−1
. (6)
Note that these expressions resemble the ordinary least squares solution to the maximum likelihood estima-tion for (auto-) regressions with complete data with the difference that the sufficient statistics are replacedby their expectations.
The (j + 1)-iteration covariance matrices are computed as the expectations of sums of squared residualsconditional on the updated estimates of Λ and A:13
R(j + 1) = diag
(1T
T∑
t=1
Eθ(j)
[(yt − Λ(j + 1)ft
)(yt − Λ(j + 1)ft
)′|ΩT
])(7)
= diag
(1T
(T∑
t=1
Eθ(j)
[yty
′t|ΩT
]− Λ(j + 1)
T∑
t=1
Eθ(j)
[fty
′t|ΩT
]))
and
Q(j + 1) =1T
(T∑
t=1
Eθ(j)
[ftf
′t |ΩT
]− A(j + 1)
T∑
t=1
Eθ(j)
[ft−1f
′t |ΩT
])
. (8)
When yt does not contain missing data, we have that
Eθ(j) [yty′t|ΩT ] = yty
′t and Eθ(j) [ytf
′t |ΩT ] = ytEθ(j) [f ′
t |ΩT ] . (9)
Finally, the conditional moments of the latent factors, Eθ(j) [ft|ΩT ], Eθ(j) [ftf ′t |ΩT ], Eθ(j)
[ft−1f ′
t−1|ΩT
]
and Eθ(j)
[ftf ′
t−1|ΩT
], can be obtained through the Kalman smoother for the state space representation:
yt = Λ(j)ft + εt , εt ∼ i.i.d. N (0, R(j)) ,
ft = A(j)ft−1 + ut , ut ∼ i.i.d. N (0, Q(j)) , (10)
see Watson and Engle (1983).
However, when yt contains missing values we can no longer use (9) when developing the expressions (5)and (7). Let Wt be a diagonal matrix of size n with ith diagonal element equal to 0 if yi,t is missing andequal to 1 otherwise. As shown in the Appendix, Λ(j + 1) can be obtained as
vec(Λ(j + 1)
)=
(T∑
t=1
Eθ(j)
[ftf
′t |ΩT
]⊗ Wt
)−1
vec
(T∑
t=1
WtytEθ(j)
[f ′
t |ΩT
])
. (11)
Intuitively, Wt works as a selection matrix, so that only the available data are used in the calculations.Analogously, the expression (7) becomes
R(j + 1) = diag
(1T
T∑
t=1
(Wtyty
′tW
′t − WtytEθ(j)
[f ′
t |ΩT
]Λ(j + 1)′Wt − WtΛ(j + 1)Eθ(j)
[ft|ΩT
]y′
tWt
+ WtΛ(j + 1)Eθ(j)
[ftf
′t |ΩT
]Λ(j + 1)′Wt + (I − Wt)R(j)(I − Wt)
)). (12)
12A sketch of how these are derived is provided in the Appendix, see also e.g. Watson and Engle (1983) and Shumway andStoffer (1982).
13Note that L(θ, θ(j)) does not have to be maximised simultaneously with respect to all the parameters. The procedureremains valid if M-step is performed sequentially, i.e. L(θ, θ(j)) is maximised over a subvector of θ with other parametersheld fixed at their current values, see e.g. McLachlan and Krishnan (1996), Ch. 5.
11ECB
Working Paper Series No 1189May 2010
following expressions for Λ(j + 1) and A(j + 1):12
Λ(j + 1) =
(T∑
t=1
Eθ(j)
[ytf
′t |ΩT
])(
T∑
t=1
Eθ(j)
[ftf
′t |ΩT
])−1
, (5)
A(j + 1) =
(T∑
t=1
Eθ(j)
[ftf
′t−1|ΩT
])(
T∑
t=1
Eθ(j)
[ft−1f
′t−1|ΩT
])−1
. (6)
Note that these expressions resemble the ordinary least squares solution to the maximum likelihood estima-tion for (auto-) regressions with complete data with the difference that the sufficient statistics are replacedby their expectations.
The (j + 1)-iteration covariance matrices are computed as the expectations of sums of squared residualsconditional on the updated estimates of Λ and A:13
R(j + 1) = diag
(1T
T∑
t=1
Eθ(j)
[(yt − Λ(j + 1)ft
)(yt − Λ(j + 1)ft
)′|ΩT
])(7)
= diag
(1T
(T∑
t=1
Eθ(j)
[yty
′t|ΩT
]− Λ(j + 1)
T∑
t=1
Eθ(j)
[fty
′t|ΩT
]))
and
Q(j + 1) =1T
(T∑
t=1
Eθ(j)
[ftf
′t |ΩT
]− A(j + 1)
T∑
t=1
Eθ(j)
[ft−1f
′t |ΩT
])
. (8)
When yt does not contain missing data, we have that
Eθ(j) [yty′t|ΩT ] = yty
′t and Eθ(j) [ytf
′t |ΩT ] = ytEθ(j) [f ′
t |ΩT ] . (9)
Finally, the conditional moments of the latent factors, Eθ(j) [ft|ΩT ], Eθ(j) [ftf ′t |ΩT ], Eθ(j)
[ft−1f ′
t−1|ΩT
]
and Eθ(j)
[ftf ′
t−1|ΩT
], can be obtained through the Kalman smoother for the state space representation:
yt = Λ(j)ft + εt , εt ∼ i.i.d. N (0, R(j)) ,
ft = A(j)ft−1 + ut , ut ∼ i.i.d. N (0, Q(j)) , (10)
see Watson and Engle (1983).
However, when yt contains missing values we can no longer use (9) when developing the expressions (5)and (7). Let Wt be a diagonal matrix of size n with ith diagonal element equal to 0 if yi,t is missing andequal to 1 otherwise. As shown in the Appendix, Λ(j + 1) can be obtained as
vec(Λ(j + 1)
)=
(T∑
t=1
Eθ(j)
[ftf
′t |ΩT
]⊗ Wt
)−1
vec
(T∑
t=1
WtytEθ(j)
[f ′
t |ΩT
])
. (11)
Intuitively, Wt works as a selection matrix, so that only the available data are used in the calculations.Analogously, the expression (7) becomes
R(j + 1) = diag
(1T
T∑
t=1
(Wtyty
′tW
′t − WtytEθ(j)
[f ′
t |ΩT
]Λ(j + 1)′Wt − WtΛ(j + 1)Eθ(j)
[ft|ΩT
]y′
tWt
+ WtΛ(j + 1)Eθ(j)
[ftf
′t |ΩT
]Λ(j + 1)′Wt + (I − Wt)R(j)(I − Wt)
)). (12)
12A sketch of how these are derived is provided in the Appendix, see also e.g. Watson and Engle (1983) and Shumway andStoffer (1982).
13Note that L(θ, θ(j)) does not have to be maximised simultaneously with respect to all the parameters. The procedureremains valid if M-step is performed sequentially, i.e. L(θ, θ(j)) is maximised over a subvector of θ with other parametersheld fixed at their current values, see e.g. McLachlan and Krishnan (1996), Ch. 5.
11ECB
Working Paper Series No 1189May 2010
following expressions for Λ(j + 1) and A(j + 1):12
Λ(j + 1) =
(T∑
t=1
Eθ(j)
[ytf
′t |ΩT
])(
T∑
t=1
Eθ(j)
[ftf
′t |ΩT
])−1
, (5)
A(j + 1) =
(T∑
t=1
Eθ(j)
[ftf
′t−1|ΩT
])(
T∑
t=1
Eθ(j)
[ft−1f
′t−1|ΩT
])−1
. (6)
Note that these expressions resemble the ordinary least squares solution to the maximum likelihood estima-tion for (auto-) regressions with complete data with the difference that the sufficient statistics are replacedby their expectations.
The (j + 1)-iteration covariance matrices are computed as the expectations of sums of squared residualsconditional on the updated estimates of Λ and A:13
R(j + 1) = diag
(1T
T∑
t=1
Eθ(j)
[(yt − Λ(j + 1)ft
)(yt − Λ(j + 1)ft
)′|ΩT
])(7)
= diag
(1T
(T∑
t=1
Eθ(j)
[yty
′t|ΩT
]− Λ(j + 1)
T∑
t=1
Eθ(j)
[fty
′t|ΩT
]))
and
Q(j + 1) =1T
(T∑
t=1
Eθ(j)
[ftf
′t |ΩT
]− A(j + 1)
T∑
t=1
Eθ(j)
[ft−1f
′t |ΩT
])
. (8)
When yt does not contain missing data, we have that
Eθ(j) [yty′t|ΩT ] = yty
′t and Eθ(j) [ytf
′t |ΩT ] = ytEθ(j) [f ′
t |ΩT ] . (9)
Finally, the conditional moments of the latent factors, Eθ(j) [ft|ΩT ], Eθ(j) [ftf ′t |ΩT ], Eθ(j)
[ft−1f ′
t−1|ΩT
]
and Eθ(j)
[ftf ′
t−1|ΩT
], can be obtained through the Kalman smoother for the state space representation:
yt = Λ(j)ft + εt , εt ∼ i.i.d. N (0, R(j)) ,
ft = A(j)ft−1 + ut , ut ∼ i.i.d. N (0, Q(j)) , (10)
see Watson and Engle (1983).
However, when yt contains missing values we can no longer use (9) when developing the expressions (5)and (7). Let Wt be a diagonal matrix of size n with ith diagonal element equal to 0 if yi,t is missing andequal to 1 otherwise. As shown in the Appendix, Λ(j + 1) can be obtained as
vec(Λ(j + 1)
)=
(T∑
t=1
Eθ(j)
[ftf
′t |ΩT
]⊗ Wt
)−1
vec
(T∑
t=1
WtytEθ(j)
[f ′
t |ΩT
])
. (11)
Intuitively, Wt works as a selection matrix, so that only the available data are used in the calculations.Analogously, the expression (7) becomes
R(j + 1) = diag
(1T
T∑
t=1
(Wtyty
′tW
′t − WtytEθ(j)
[f ′
t |ΩT
]Λ(j + 1)′Wt − WtΛ(j + 1)Eθ(j)
[ft|ΩT
]y′
tWt
+ WtΛ(j + 1)Eθ(j)
[ftf
′t |ΩT
]Λ(j + 1)′Wt + (I − Wt)R(j)(I − Wt)
)). (12)
12A sketch of how these are derived is provided in the Appendix, see also e.g. Watson and Engle (1983) and Shumway andStoffer (1982).
13Note that L(θ, θ(j)) does not have to be maximised simultaneously with respect to all the parameters. The procedureremains valid if M-step is performed sequentially, i.e. L(θ, θ(j)) is maximised over a subvector of θ with other parametersheld fixed at their current values, see e.g. McLachlan and Krishnan (1996), Ch. 5.
Source: Banbura M., and Modugno, M (2010)
Outcomes
News Contribuion
8Investment in ”Real Time” & ”High Definition”: A Big Data approach
TURKEY: VARIABLES IN MONTHLY GDP DFM
Har
dD
ata
(M &
D)
Soft
(M)
Fin
(W)
Big
Dat
a (D
)Source: Own elaboration
Investment Big Data in a Nowcasting Model (DFM): Variables & Releases
Jan Feb Mar Apr May Jun July Aug SepGFCF
Capital Goods Production
Non-metal M. Production
Capital Goods Imports
Commercial Vehicle Sales 1 2Real Sector Confidence
Corporate Lonas
Big Data Investment
2020
TURKEY: VARIABLES IN MONTHLY INVESTMENT DFM
Jan Feb Mar Apr May Jun July Aug SeptGDP
Industrial Production
Non-metal Mineral Production
Auto Sales
Number of Employed
Number of Unemployed
Auto Imports
Auto Exports
Electricity Production
Manufacturing PMI
Real Sector Confidence
Total Loans growth 13-week
Bog Data Total Consumption Indicator
Bog Data Total Investment Indicator
2020
Big Data Investment
Big Data Consumption
9Investment in ”Real Time” & ”High Definition”: A Big Data approach
TURKEY: OUT-OF-SAMPLE ERROR GDP MODEL
Source: Own Elaboration
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
14%
Mar
-16
Jun-
16
Sep
-16
Dec
-16
Mar
-17
Jun-
17
Sep
-17
Dec
-17
Mar
-18
Jun-
18
Sep
-18
Dec
-18
Mar
-19
Jun-
19
Sep
-19
Dec
-19
Mar
-20
TURKSTAT GDP
Standard Dynamic Factor Model (DFM)
DFM + Big Data Investment
-25%
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
Mar
-16
Jun-
16
Sep
-16
Dec
-16
Mar
-17
Jun-
17
Sep
-17
Dec
-17
Mar
-18
Jun-
18
Sep
-18
Dec
-18
Mar
-19
Jun-
19
Sep
-19
Dec
-19
Mar
-20
TURKSTAT Investment Expenditures
Standard Dynamic Factor Model (DFM)
DFM + BBVA Investment Index
TURKEY: OUT-OF-SAMPLE ERROR INVESTMENT MODEL
Investment Big Data in a Nowcasting Model (DFM): Forecasting Accuracy
10Investment in ”Real Time” & ”High Definition”: A Big Data approach
TURKEY: NOWCASTING FINANCIAL CRISIS (SEPT 2018) & COVID CRISIS (MAR 2020)(quasi real time nowcasting with and without Big Data Indexes vs Benchmark)**
Financial Crisis (September 2018) COVID-19 (March 2020)
The model with Big Data investmentStart to signal the deceeleration moretan a motnh before
The model with Big Data Consumption Reactedinmediately signalling theDeep and the Sharp recovery
Investment Big Data in a Nowcasting Model (DFM): Anticipation
11Investment in ”Real Time” & ”High Definition”: A Big Data approach
0.0
1.0
2.0
3.0
4.0
5.0
Indu
stria
l Pro
duct
ion
(M)
Big
Data
Inve
stnm
ent (
D)
Une
mpl
oym
ent /
d)
Car
Impo
rts (M
)
Car
Sal
es (M
)
PMI M
anuf
ac (M
)
Eect
ricity
Pro
duct
ion
(D)
Cem
ent P
rod
(M)
Cre
dit G
rowt
h (W
)
Empl
oym
ent (
M)
Big
Data
Con
sum
ptio
n (D
)
Busi
ness
Con
fiden
ce (M
)
Car
Exp
orts
(M)
M1/2 M2/3 M3/4 M4/5 Average
DFM News Contributions(Unbalanced Sample)
Source: Own Estimations Source: Own Elaboration
DFM News Contributions correcting Prevalece Bias(Maintaining individually all the variables for the sample of Big data information)
Investment Big Data in a Nowcasting Model (DFM): News & Prevalence Bias
12Investment in ”Real Time” & ”High Definition”: A Big Data approach
-50%
-40%
-30%
-20%
-10%
0%
10%
20%
30%
40%
50%
2-M
ar12
-Mar
22-M
ar1-
Apr
11-A
pr21
-Apr
1-M
ay11
-May
21-M
ay31
-May
10-J
un20
-Jun
30-J
un10
-Jul
20-J
ul30
-Jul
9-A
ug19
-Aug
29-A
ug8-
Sep
18-S
ep28
-Sep
8-O
ct18
-Oct
28-O
ct7-
Nov
Machinery Construction Total Investment
-60%
-40%
-20%
0%
20%
40%
60%
80%
2-M
ar12
-Mar
22-M
ar1-
Apr
11-A
pr21
-Apr
1-M
ay11
-May
21-M
ay31
-May
10-J
un20
-Jun
30-J
un10
-Jul
20-J
ul30
-Jul
9-A
ug19
-Aug
29-A
ug8-
Sep
18-S
ep28
-Sep
8-O
ct18
-Oct
28-O
ct7-
Nov
Goods Services Total Consumption
Results: Investment in Real Time will help policy makers to react faster
Source: Own Elaboration
TURKEY: BIG DATA CONSUMPTION & INVESTMENT(7-day cum. YoY nominal in Cons., 28-day cum. YoY nominal in Invest.)
BIG DATA CONSUMPTION BIG DATA INVESTMENT
2Q-20 3Q-20 4Q-20 2Q-20 3Q-20 4Q-20
13Investment in ”Real Time” & ”High Definition”: A Big Data approach
TURKEY:GB-BBVA BIG DATA INVESTMENT HEAT MAP(3mm avg YoY nominal)
Source: Own Elaboration
Results: The "High Definition" dimension will allow policymakers todifferentiate shocks and design more targeted policies
TURKEY:GB-BBVA BiG DATA INVESTMENTS GEO-MAPS RECOVERY AFTER THE COVID(Change in YoY investment before, during and after the lockdowns by Covid)
20Activities & 81Province in Real Time & High Definition
14Investment in ”Real Time” & ”High Definition”: A Big Data approach
Conclusions & further Research
- We present a novel approach to estimate Investment in “Real Time & HighDefinition” from the analysis of a Bank´s Big Data (BBVA)
- The Investment index improves the properties of a Standard Nowcasting Modelin terms of forecasting accuracy, anticipation and news.
- The “High Definition” dimension can help to design targeted policies
- We cross validate the results through the high correlations with national accountsand high frequency proxies for Turkey and other countries.
- The characteristics of Big data Information (detailed but short history) advocates forthe use of non linear and/or regularization techniques (Further Research)
15Investment in ”Real Time” & ”High Definition”: A Big Data approach
References
• Chetty, R., Friedman, J. N., Hendren, N., & Stepner, M. (2020). How Did COVID-19 and Stabilization Policies Affect Spending and Employment? A New Real-Time Economic Tracker Based on Private Sector Data. Working Paper.
• Chronopoulos, D. K., Lukas, M., & Wilson, J. O. S. (2020). Consumer SpendingResponses to the COVID-19 Pandemic: An Assessment of Great Britain. WorkingPaper 20-012.
• Carvalho, V,Hansen,S,Ortiz,A, Garcia,JR, Rodrigo,T, Rodriguez Mora,S P,Ruiz(2020). Tracking the Covid-19 crisis with high resolution transaction data”. CEPR DPNo 14642
• Cox, N., Ganong, P., Noel, P., Vavra, J., Wong, A., Farrell, D., & Greig, F. (2020).Initial Impacts of the Pandemic on Consumer Behavior: Evidence from Linked Income,Spending, and Saving Data.
• Eurostat (2013) Handbook on quarterly national accounts
• Gezici F & Burçin Yazgı Walsh & Sinem Metin Kacar, 2017. "Regional and structuralanalysis of the manufacturing industry in Turkey," The Annals of Regional Science,Springer;Western Regional Science Association, vol. 59(1), pages 209-230, July.
• Modugno, M., B. Soybilgen, and E. Yazgan (2016). Nowcasting Turkish GDP andNews Decomposition. International Journal of Forecasting 32 (4), 1369–1384.
• Surico, P., Kanzig, D., & Hacioglu, S. (2020). Consumption in the Time of COVID-19:Evidence from UK Transaction Data. CEPR Discussion Paper 14733.
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Investment in “Real Time” and“High Definition”: A Big Data Approach
November 2020
2020 Conference on Nontraditional Data & Statistical LearningBanca d’ Italia and Federal Reserve Board
Ali.B. Barlas, Seda Güler, Alvaro Ortiz & Tomasa Rodrigo