Condiciones de trabajo en el proceso de la línea “Princess Natural”

Our main research question is whether the sentiment of different industry seg- ments has predictive power for macro-economic indicators. Our methodology is also applicable to other ways of segmenting firms, as region in which the are lo- cated or according to their company size. For our data, there are 10 regions and three company sizes. We re-estimate the 8 ARX models and perform the Granger Causality tests for the 20 regional blocks (i.e. 10 blocks for the Business Survey, 10 blocks for the Bank Survey). Likewise, we re-estimate the 8 ARX models and perform the Granger Causality tests for the 6 company size blocks (i.e. 3 blocks for the Business Survey, 3 blocks for the Bank Survey).

The forecast performance of the Granger Lasso test obtained with either indus- try, region or company size segments is very similar. We compare Mean Absolute Forecast Errors as in Table 3.7. For the regional segments, the Granger Lasso test is the best performing selection technique and attains the lowest value of the MAFE in 60% of the cases (24 out of 40). Similarly for the company size segments

3.9. Discussion 67

where the Granger Lasso test leads towards the lowest MAFE in 68% of the cases (27 out of 40).

We again find business sentiment to have more incremental predictive power than bank sentiment. Furthermore, Germany’s largest geo-economical regions (i.e. Ruhr area and the Southern states) have most incremental predictive power for the macro-economic indicators to which their day-to-day business contributes most, i.e. IP-A1, IP-A2, IP-M, IP-E and IP-CaGo, IP-CoGo respectively. Finally, small- and medium-sized companies have more incremental predictive power than large companies. Germany is dominated by small- to medium-sized companies who are global market leaders in their segments, and, hence, those might be best at evaluating Germany’s economy.

3.9

Discussion

This paper presents a high-dimensional Granger Causality test. It detects the most predictive industry segments for future macro-economic developments. For this purpose, we use both business and bank sentiment surveys answered by firms across Germany. Not all industry-specific sentiment indicators are equally predic- tive for all macro-economic indicators. Industries contain most predictive power for the macro-economic indicators most closely tied to their day-to-day business activities.

Our forecast exercise shows that important gains in forecast accuracy can be obtained by not using all industry segments, but by first selecting the most pre- dictive ones using the Granger Lasso test selection technique. In high-dimensional settings, a lot of noise might be present. By selecting predictor variables, a more parsimonious model with less noise is obtained. Note that losing information is a potential risk of selecting predictor variables, hence, the need for research on appropriate selection methods. The selection of the most pertinent industry segments also provides important information for institutes conducting these sen- timent surveys. For instance, instead of equally spreading respondents among all segments, the number of respondents in predictive segments could be increased, whereas the number of respondents in non-predictive segments could be decreased. Alternatively, non-predictive segments could even be completely discarded, which provides an opportunity to obtain cost savings.

The identification of pertinent respondents also applies to consumer sentiment surveys. In the large literature on consumer sentiment, this topic has received lit- tle attention. We perform a similar exercise as described in this paper using a

68 High-dimensional Granger Causality

consumer sentiment survey data set from the National Bank of Belgium. Senti- ment indicators are available for different classes of consumers’ net disposable in- come, profession, employment status, education, age and gender. We study their predictive power for several retail trade indicators. The profession, education, and age sentiment indicators contain most predictive power. Again, important gains in forecast accuracy can be obtained by first selecting the most predictive sentiment indicators (for a specific target variable of interest) instead of using all indicators.

We use a high-dimensional Granger Causality approach to study the predic- tive power of sentiment data collected via surveys. One could consider social media as an alternative channel to collect sentiment data. While their role in collecting consumer sentiment has received considerable attention (e.g. Pang and Lee, 2008, Asur and Huberman, 2010, Stieglitz and Dang-Xuan, 2013), their role in collecting business sentiment has received limited to no attention. It should be noted that collecting data via social media poses sampling issues since only a subpopulation (i.e. the participants of these social media) of all respondents is reached. In contrast, data collected via surveys are sent out to a random sample of all respondents.

While we study the predictive power of sentiment indicators for future macro- economic growth, another interesting research question is whether sentiment indi- cators and macro-economic indicators move together in the long-run. This could be addressed using Cointegration analysis, which aims at detecting long-run re- lationships between several time series (see L¨utkepohl, 1993 for an introduction,

¨

Ostermark, 2001 or Musti and D’Ecclesia, 2008 for an application. Testing for cointegration in high-dimensions is, however, an open research area (e.g. Breitung and Cubadda, 2011) and ideas similar to the once introduced in this paper could serve as a starting point.

Finally, we need to further deepen our understanding on the usefulness of bank sentiment. It would be interesting to investigate if this sentiment differs between, for instance, countries that are more or less severely hit by banking crises, and developed or developing countries. The study of sentiment with respect to the banking sector opens a new area of research on sentiment surveys.

Chapter 4

Forecasting using sparse

cointegration

Abstract

This paper proposes a sparse cointegration method. Cointegration anal- ysis is used to estimate the long-run equilibrium relations between several time series. The coefficients of these long-run equilibrium relations are the cointegrating vectors. We provide a sparse estimator of the cointegrating vectors. Sparse estimation means that some elements of the cointegrating vectors are estimated as exactly zero, improving interpretability. The sparse estimator is applicable in high-dimensional settings, where the length of the time series is short compared to the number of time series. Our method achieves better estimation accuracy and forecast accuracy than the tradi- tional Johansen method in sparse and/or high-dimensional settings. We use the sparse method for interest rate growth forecasting and consumption growth forecasting. The sparse cointegration method leads to important gains in forecast accuracy compared to the Johansen method.

4.1

Introduction

High-dimensional data sets containing thousands of time series are commonly available and accessible at reasonable cost [Stock and Watson, 2002, Fan et al., 2011]. There has been a considerable amount of recent work exploiting the large amount of information in these data sets for forecasting purposes. To handle the

70 Sparse cointegration

dimensionality, large time series models, containing a large number of time series relative to the time series length, have been considered. Common approaches are, among others, Factor Models (e.g. Stock and Watson, 2002), Bayesian Vec- tor AutoRegressive (VAR) Models (e.g. Banbura et al., 2010), or Reduced-Rank VAR Models (e.g. Carriero et al., 2011, Bernardini and Cubadda, 2015). Typ- ically, these authors do not account for cointegration. Instead, the time series are either transformed in order to achieve stationarity [Bernardini and Cubadda, 2015] or the (non)-stationarity is accounted for in the prior distribution of the autoregressive parameters [Banbura et al., 2010]. In cointegration analysis, long- run equilibrium relations between several time series, often implied by economic theory, are estimated.

This paper develops a cointegration method for high-dimensional time se- ries. The Vector Error Correcting Model (VECM) (e.g. L¨utkepohl, 2007) is used to estimate and test for the cointegration relations. Various cointegration tests are existing (e.g. Engle and Granger, 1987, Phillips and Ouliaris, 1990), among which the cointegration test of Johansen [1988] has become most popu- lar. Johansen’s Maximum Likelihood approach has, however, some limitations. In high-dimensional settings, where the number of time series is large compared to the length of the time series, the estimation imprecision will be large. Jo- hansen’s approach is based on the estimation of a VAR model and a canonical correlation analysis. A drawback of the VAR is that its number of parameters increases quadratically with the number of included time series. Consequently, regression parameters are estimated inaccurately if only a limited number of time points is available. When the number of time series exceeds the time series length, Johansen’s approach can not even be applied.

We introduce a Penalized Maximum Likelihood (PML) approach to estimate the cointegrating vectors in a sparse way, i.e. some of its components are estimated as exactly zero. Sparse estimators show good performance in various fields such as economics (e.g. Fan et al., 2011), macro-economics (e.g. Korobilis, 2013; Liao and Phillips, 2015), finance (e.g. Zhou et al., 2014), or biostatistics (e.g. Friedman, 2012). A sparse cointegration method is useful for several reasons. First, sparsity facilitates model interpretation since only a limited number of time series, those corresponding to the non-zero coefficients, enter the estimated long-run equilibrium relations. Second, sparsity improves forecast performance through variance reduction. Third, the sparse approach, in contrast to Johansen’s Maximum Likelihood approach, can be applied when the number of time series exceeds the time series length.