Austrian Inflation Rate

Transcription

1 Austrian Inflation Rate Course of Econometric Forecasting Nadir Shahzad Virkun Tomas Sedliacik

2 Goal and Data Selection Our goal is to find a relatively accurate procedure in order to forecast the Austrian inflation rate. Underlying Data Series: Monthly inflation rate for the period Jan 1987 Dec 2006 calculated as logarithmic differences of the Austrian Consumer Price Index: Xt = log ( Pt / Pt-1 ) <=> Xt = log(pt) - log(pt-1)

3 Separation of the Data In-Sample: Jan 1987 Dec 2001 (180 observations) Out-of-Sample: Jan 2002 Dec 2006 (60 observations)

4 Objective Criteria Minimize Mean Squared Error (MSE) Information Criteria: Akaike Information Criterion Schwarz Criterion Properties of the Prediction Errors (distribution, autocorrelation)

5 Forecasting Method Selection Both model free and model based procedures will be applied Characteristics of the data series Discrete Statistics (normality) Visual inspection (trend, seasonality) Autocorrelation Augmented Dickey-Fueller (Stationarity)

6 Visual Inspection

7 Visual Inspection From the visual inspection the following issues seem to be quite obvious: Negligible trend Seasonality (cycle: 12) Change in behavior around 1997 Quite homogenous (regular) in the first part Loss of regularity in the second part

8 Model-free procedures Exponential Smoothers are unable to capture seasonal elements of the series No Trend: DES would probably bring no advantage compared to SES Holt-Winters are suggested to capture the seasonality (cycle: 12) Negativity: Multiplicative version not possible => only HW additive applied

9 Simple Exponential Smoothing * = (very strong smoothing) MSE = (for the whole sample) MSE = (out of sample) Because of the constant prediction the MSE out of sample even exceeds the standard deviation of the series

10 Simple Exponential Smoothing

11 Additive Holt-Winters (s=12) * = 0.05 ; * = 0 ; * = No trend; strong seasonality MSE = (for the whole sample) MSE = (out of sample) Out of sample even worse than the constant prediction of SES; predicted seasonal effects seem to go to the wrong direction

12 Additive Holt-Winters (s=12)

13 Model Based Procedures Selection of an appropriate model requires to check some data properties Most important characteristics to check: Stationarity (Augmented Dickey-Fuller) Lag dependencies (ACF, PACF)

14 Check for stationarity ADF statistics for 4 lagged differences equals The 1% critical value equals Therefore the null hypothesis (that there is a unit root present) can be rejected at a confidence level of over 99% => stationary data series

15 Check for Lag Dependencies

16 Model Fitting As the pic. shows that there are severe interdependencies in the data and also 12th, 24th and 36th lags are important see the seasonal impact We employed different models to observe the true model as data generating process, namely AR, MA, ARMA and ARMA with seasonalities Since our model free part (HW additive) suggest that the data is with strong seasonalities We also get the best fit with ARMA (4,4) with seasonal AR and MA components

17 ARMA (4,4) with Seasonal AR and MA terms

18 In Sample Estimation and Residuals R e s i d u a l A c tu a l F i tte d

19 Correlogram of Residuals of Fitted Model

20 Out of Sample Forecast Forecas t: INFLF Ac tual: INFL Forecas t sample: 2002M M12 Included observations: 60 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion INFLF

21 Out of Sample Actual and Forecast IN F L IN F L F

22 Forecast with Improved Model F orec as t: INFLF Ac tual: INF L Forec as t s am ple: 2002M M12 Included obs ervations: 60 R oot Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality C oeffic ient Bias Proportion Variance Proportion C ovarianc e Proportion INFLF

23 Comments Despite the fact the model fitted the data nicely but the model performed out of sample poorly. In order to get improved forecasting, we fitted a model with boh AR and MA terms of lag order 2 and 6 and SAR and SMA of lag 12 This model improved the fit in terms of AIC, SIC, R squared and sum of squared errors and give a white noise residual process but it also performed poorly out of sample and missed completely out of sample trudges as our benchmark model did. If we examine the predictions of both the models we see both are two smoothed than actual and mostly the predictions responded troughs with peak and peaks with troughs.

24 Comments (Cntd.) But improved model, improved as per listed our loss function criterion, that is, Mean square error, which is as compared to fitted model, that is, One reason for poor prediction of our models is that the strong seasonal impact that is present till 1996 is missing in last 10 years. The estimated parameters are too looped with seasonality that they couldnot give a better prediction for a period where seasonality is not as substantial as before. We also argue the changing dynamics of CPI log price changes for Austria are more to do with the entry of Austria in EU and EMU and later to the introduction of euro, which require strict price stability as described in the mission statement of ECB.

25 Multivariate Modelling Potential relationship to other variables Independent variables used: 12-Month Euribor rate Austrian Production Index Limited availability => shorter series ( ) Stationarity testing => finally first differences of both variables used

26 Cross-Correlation: Diff_Euribor

27 Cross-Correlation: Diff_API

28 Types of Models used Inflation series expressed only by the explanatory variables VAR-Models With each variable separately Both combined within one model VARMA-Models With each variable separately Both combined within one model

29 Model Results: Criteria Model OOS-MSE Akaike IC R-squared norm. of err. var6_deur6 0, ,39 0,26 0,65 var6_dindex12 0, ,71 0,52 0,92 var6_deur12_dindex12 0, ,6 0,67 0,75 varma_deur 0, ,11 0,65 0,85 varma_dindex 0, ,07 0,52 0,42 varma_deur_dindex 0, ,83 0,5 0,68 arma(1,2,6,12) 0, ,78 0,42 0,93 arma_special 0, ,01 0,62 0,43

30 Uni- and Multivariate Forecast

31 Conclusion No model dominating the others regarding all criteria Multivariate is not automatically better than univariate Limited reliability; longer series might be required Changes in behavior caused by external events (such as political decisions) reduce the forecastability

32 Thank You for Your Attention