Testing the Out-of-Sample Forecasting Ability of a Financial Conditions Index for South Africa 

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CHAPTER 3: TESTING THE OUT-OF-SAMPLE FORECASTING ABILITY OF A FINANCIAL CONDITIONS INDEX FOR SOUTH AFRICA15

INTRODUCTION

The previous chapter constructed a financial conditions index (FCI) for South Africa to capture in a single indicator the full spectrum of financial variables that affect the South African economy. The aim of this chapter is to investigate whether that FCI can act as an „early   warning   indicator‟   for   impending   macroeconomic   instability   caused   by deteriorating  financial  conditions  by  means  of  out-of-sample  forecasting  tests.  The premise here is based on the fact that asset prices (a major component of the FCI) are regarded as useful predictors of inflation and output growth (Stock and Watson, 2003)16. However, forecasts based on individual asset prices tend to be unstable, and combination approaches are preferable (Stock and Watson, 2003). To this end I test whether the estimated FCI does better than its individual financial components in forecasting key macroeconomic variables, namely output growth, inflation and an interest rate.
This  forecasting  exercise  is  conducted  with  caution,  and  the  techniques  are  chosen specifically  to  hopefully  address  issues  associated  with  the  use  of  asset  prices  in forecasting real economic activity noted by Stock and Watson (2003:801) (remembering that the FCI largely comprises asset prices): namely, the “underlying relations themselves depend on economic policies, macroeconomic shocks, and specific institutions and thus evolve  in  ways  that  are  sufficiently  complex  that  real-time  forecasting  confronts considerable model uncertainty”. The concept „forecast encompassing‟ is used to examine the forecasting ability of these variables following Rapach and Weber (2004). They consider the forecasting power of ten financial variables with respect to real GDP growth and industrial production growth in the US over the period 1985M01 to 1999M04, to test and complement a similar study by Stock and Watson (2003)17. The forecast encompassing approach used in this chapter is based  on  two  sets  of  out-of-sample  forecasts  for  output  growth,  inflation,  and  the Treasury Bill yield. The two forecasts are obtained from an autoregressive distributed lag (ARDL) model including one financial variable at a time, and a benchmark autoregressive (AR) model. An optimal composite forecast is formed as the convex combination of these two forecasts and is interpreted as follows: if the optimal weight attached to the ARDL model‟s forecast is zero, then the ARDL model does not contain information that is useful for forecasting the chosen macroeconomic variable apartfromtheinformationalready contained in  the  AR  benchmark  model.  In  other  words,  the  AR  model‟s  forecasts encompass those of the ARDL model. Instead, if the optimal weight attached to the ARDL model‟s forecast is larger than zero, then the ARDL model doescontain information that is  useful  for  forecasting  the  chosen  macroeconomic  variables  in  addition  to  the information already contained in the AR benchmark model. The generic null hypothesis for  these  tests  can  then  be  stated  as:  the  AR  benchmark  out-of-sample  forecast encompasses the ARDL out-of-sample forecast (where the ARDL model includes the selected financial variable or the FCI); i.e. that the AR model is the “better” forecasting model,  which  implies  that  the  selected  financial  variable  or  FCI  is  not  relevant  in forecasting the chosen macroeconomic variable.
So  for  each  financial  variable  and  the  FCI,  recursive  out-of-sample  forecasts  of manufacturing output growth, inflation and the Treasury Bill yield are constructed over the out-of-sample period of 1986M01–2012M01, using an ARDL model that includes the chosen financial variable or FCI as an explanatory variable. As suggested by Rapach and Weber (2004), I test the above null hypothesis of an encompassing AR model forecast using various statistics proposed by Harvey, Leybourne and Newbold (1998) and Clark and McCracken (2001).
The  remainder  of  the  chapter  is  organised  as  follows:  Section  3.2  presents  a  brief discussion of the data used in the forecast encompassing exercises; while Section  3.3 presents  Rapach  and  Weber‟s  (2004)  econometric  methodology  used  in  the  forecast encompassing tests, including derivations of the five test statistics used for inference. The empirical  out-of-sample  forecast  results  are  presented  in  Section  3.4,  along  with adjustments  made  to  the  test  statistics  so  as  to  account  for  data-mining,  as  well  as discussions  of  the  individual  predictors‟  economic  significance  (for  those  predictors surviving  data-mining),  and  Section  3.5  provides  the  forecasting  performance  of  the estimated FCI. Section 3.6 concludes the chapter.

DATA

In compiling the FCI in the previous chapter, I choose series that encompass measures in levels, as well as volatility measures. The data series included in the compilation of the FCI are found in Table 1 in Chapter 2, and are discussed in Section 2.5. The data set covers  the  sample  of  1966M02  –  2012M01.  The  data  series  used  in  the  forecasting exercises  in  this  chapter  include:  the  estimated  FCI;  each  of  its  sixteen  individual component series; a measure of output growth – the month-on-month rate of change in South Africa‟s Manufacturing Production Index; a measure of inflation – the month-on- month rate of change in the CPI; and the 3-month Treasury Bill yield. The latter three series are the macroeconomic variables with respect to which I test the FCI‟s forecasting ability.  Figure  2 shows the three  macroeconomic  series  compared graphically  to  the estimated FCI.

ECONOMETRIC METHODOLOGY

The forecast encompassing test used in this research follows Rapach and Weber (2004), and more details on the econometric methodology can be found in that paper. I consider the unrestricted ARDL model:
where is the variable of interest to be forecasted (manufacturing growth, Treasury Bill yield and inflation), q1   and q2 are the ARDL lags, is the FCI or one of the sixteen financial variables used in the construction of the FCI, and his the forecast horizon (set to a maximum of 24 months in this instance)18. The following recursive procedure is used to simulate the out-of-sample forecasting ability of the individual financial data series and the  FCI:  First,  divide  the  total  sample  of T observations  into  the  in-sample  period, spanning Robservations, and the out-of-sample period, spanning Pobservations (in this instance, the out-of-sample period is 1986M01–2012M01).

Theil‟s U Test

If  the  root  mean  squared  forecast  error  (RMSFE)  of  the  unrestricted  ARDL  model (RMSFEUR) is less than the RMSFE of the restricted model (RMSFER), then this model is the “better” forecasting model with lower forecasting error. Therefore, if  , a result of U< 1 will indicate that the unrestricted ARDL model (i.e. the model including the financial variable or FCI as a predictor) forecasts are superior to those of the simple AR model19.

Bootstrapping Procedure

The bootstrapping procedure used to enable inference of these test statistics (from Rapach and Weber, 2004) is Clark and McCracken‟s (2007) version of Kilian (1999). Suppose, under H0: the financial variable has no forecasting power with respect to, that:
For a detailed exposition of the recursive procedure used in conducting the bootstrapping used in this chapter, refer to Rapach and Weber (2004:721-722).  Each of the four test statistics described in Equations (13), (14), (17) and (22) are calculated 500 times, resulting in empirical distributions for these statistics. The p-value for each is the proportion of the bootstrapped statistic greater than the original statistic.
The  estimated  out-of-sample  test  statistics  for  the  FCI  are  reported  in  Table  A3  in Appendix  A.5,  and  are  summarised  along  with  the  results  for  all  sixteen  financial variables in Table 5, Table 6 and Table 7 below. The results are based on the Akaike Information Criterion (AIC) and are for forecast horizons of 1, 3, 6, 9, 12, 15, 18, 21 and 24  months.  Values  for and  are  considered  from 0 up to 24. The  results  are representative of the out-of-sample period of 1986M01–2012M01. Similar results for the out-of-sample  periods 1973M01–2012M01 and  2000M01–2012M01 are  available  upon request.

CHAPTER 1: Introduction 
1.1 Background
1.1.1 Identify an appropriate FCI for South Africa
1.1.2 Use the identified FCI in forecasting exercises of major macroeconomic variables
1.1.3 Use the identified FCI in structural analysis exercises in a vector autoregression (VAR) framework
1.2 Importance and Benefits of the Study
1.3 Outline of the study
CHAPTER 2: Identifying a financial conditions index for South Africa 
2.1 Introduction
2.2 Literature review
2.3 Econometric methodology
2.4 Data
2.5 Empirical Results
2.5.1 FCI Indices
2.5.2 Evaluating the performance of FCI indices
2.6 In-sample causality testing
2.7 Conclusions
CHAPTER 3: Testing the Out-of-Sample Forecasting Ability of a Financial Conditions Index for South Africa 
3.1 Introduction
3.2 Data
3.3 Econometric Methodology
3.4 Empirical Results
3.5 An Illustration as of 2012M02
3.6 Conclusions
CHAPTER 4: Testing the Asymmetric Effects of Financial Conditions in South Africa: A Nonlinearn Vector Autoregression Approach
4.1 Introduction
4.2 Data
4.3 Econometric Methodology
4.4 Empirical Results
4.5 Conclusions
CHAPTER 5: General conclusions and areas of future research 
5.1 Introduction
5.2 Summary of key findings
5.3 Contributions of this study
5.4 Areas of future research
REFERENCES 
APPENDICES
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