Forecasting

In this section, we discuss the forecasting experiments. The forecasts are all out of sample forecasts.The focus on out of sample forecasting experiments is an attempt to simulate real time policy decision making. Since the data used are revised, the type of information available to us differs from that available to the decision maker at the central bank. Each model is composed of the price level and one possible information variable. Each forecast is a one step ahead forecast over a moving window of four years. One step ahead forecasts were preferred as a way of mimicking the horizon the central bank faces given the data. The initial estimation is done between January 1994 and December 1997. We then make a forecast for January 1998. Then the estimation sample is rolled over to start February 1994 and end January 1998 and then we make a forecast for February 1998 and so on.

We then calculate the MAPE based on ( 3.7) to decide if a variable adds significant information for forecasting or not. This decision is based on the relative performance of a benchmark model. The benchmark model used is the best fitted autoregressive model for the price level. Preliminary analysis showed that the best fit model was an AR(1) model and this can be seen from Figure 3.10 in the appendix which shows the correlation function for the price level . We therefore estimate an AR(1) model as the base model. This model is also estimated using rolling regressions over the same moving window. The higher the MAPE for a model relative to the benchmark model, the less information the additional variable has for forecasting inflation. This approach is superior to just looking at the performance of one model for our interest because it allows us to compare ’competing’ information variables. More importantly, we can check the importance of the information from the

monetary aggregates relative to information from other variables by comparing their MAPEs.

The data are used in log levels. The use of rolling regression precludes the use of co-integration in this analysis as co-integration was only identified at a few

Tab. 3.4: Mean Absolute Percentage Errors (1998-2001)

Out of sample^a

AR(1) 0.16

M1 0.115

M2 0.112

Rand exchange rate 0.104

Dollar exchange rate 0.099

Treasury bill rate 0.117

Deposit rate 0.106

Domestic debt 0.106

aThe out of sample forecasts are one step ahead forecasts with the model estimated between January 1994 and December 1997 and then forecast for the period 1998 to 2001.

horizons for most sets of variables. Forecasting with non-stationary variables produces forecast errors of similar forms as in stable cases (Luketpol (1993)).

The method used to evaluate the forecasts does not suffer from the disadvantages of say the Mean Square Error (MSE) where the error grows with the forecast horizon.

After obtaining the forecasts, we compute the percentage error for each period.

We then use these to calculate three types of MAPEs. The first is a MAPE for the entire period. Each MAPE calculated here shows the accuracy of the model over the entire forecast horizon. We show the results in table (3.4).

From the table we see that the MAPEs for all the variables are less than that of the benchmark AR(1) model. Using our decision rule, we can say that these variables have important information for forecasting inflation over the sample period. We can also say that the most important variables are the exchange rates since they have the lowest MAPEs. Conversely, the least important variables are the treasury bill rate and M1.

To see more clearly the performance evolution over the sample period of the different variables in forecasting inflation, we calculate two other types of

means. The first is a 12-month moving average of the percentage errors and a second - a cumulative mean where a mean of the percentage errors was obtained by adding one period at a time and obtaining a mean until the whole forecast horizon was covered. The results give us a time moving view of how important each variable is for forecasting inflation.

The 12-month moving averages measure the accuracy of the model in

forecasting inflation for the 12 months prior to time t. For example, if we take the first observation in the AR(1) model with a MAPE of 0.2%, we can say that using the AR(1) model to forecast inflation between December 1997 and December 1998, we would have been within 0.2% of the actual value and 0.21% of the value between January 1998 and January 1999 and so on. We graphed the obtained MAPEs in figure ( 3.7) below. To make it easier to read the graphs, we graph them in two panels so that the top panel shows results for the money aggregates and the exchange rates while the lower panel shows the interest rates and the government domestic debt. A graph that shows all the MAPEs in one figure is shown in the appendix.

All the variables’ MAPEs lie well below those of the AR(1) model through the whole sample period. The variables with the smallest MAPEs are the

exchange rates the deposit rate and domestic debt. The M2 MAPEs are also quite low especially towards the end of the sample although they increase slightly in 2001. The variable with the largest MAPEs is the treasury bill rate.

M1 does not perform very well through most of the horizon and the MAPEs of the dollar exchange rate rise in the later part of the sample.

The cumulative MAPEs are shown in figure ( 3.8). These graphs show a more long-term view of the performance of the information variables in predicting inflation. Again the top panel consist of the money variables and the exchange rates while the bottom panel consist of the interest rates and the domestic debt MAPEs. Apart from M1 which exceeds the AR(1) MAPES for a brief moment, all the MAPES lie below those of the benchmark model.The exchange rates, the deposit rate and domestic debt seem to provide the most useful information for predicting inflation while both the money aggregates

1999 2000 2001 2002 0.10

0.15

0.20 ^M2 Rand Exchange rate

A(1)

M1

Dollar Exchnage Rate

1999 2000 2001 2002

0.10 0.15

0.20 Deposit Rate

Domestic Debt

Treasury Bill Rate A(1)

Fig. 3.7: 12-Month Moving MAPES

and the treasury bill rate are not as important.

1999 2000 2001 2002

0.10 0.15 0.20 0.25

0.30 M2

Rand Exchange Rate AR(1)

M1

Dollar Exchange Rate

1999 2000 2001 2002

0.10 0.15 0.20 0.25 0.30

Deposit Rate Domestic Debt

Treasury Bill Rate AR(1)

Fig. 3.8: Cumulative MAPEs

The forecasting experiments that we conduct in this section show that over the whole sample period most of the variables examined serve as important information variables for price movements. When both long run and short run horizon experiments are considered, we find that the foreign exchange rates, the deposit rate and the domestic debt provide the most information about price movements.