Inflation Forecasts

Mumtaz: I want you to run the following exercise on the Pak and Turk data. Only use Monthly CPI and Monthly M2 data.

Let Y(t) = growth rate of CPI = log(CPI(t)/CPI(t-1))

Let X(t) = growth rate of M2 = log(M2(t)/M2(t-1))

Pick a BASE period T* -- it could be at the MIDWAY point -- half of the data. Using data from T=1,2 ..., T* estimate the base model:

Y(t) = b0 Y(t-1) + c0 M2(t-1)

For each period from T*+1 to END period, do recursive forecasting as follows:

Current Period = T*+1

Compute forecast:

Error(T*)= Y(T*) - { b0 Y(T*-1) + c0 M2(T*-1)}

Forecast Y(T*+1) = b0 Y(T*) + c0 M2(T*) + w0 Error (T*)

Initially just set w0=1/2, but arrange the EXCEL sheet in such a way that w0 can be modified and changed at each step. In other word, CREATE a column of values for w0, and we can test to make optimal changes in w0 later on.

COMPARE Forecast growth rate with actual Y(T*+1)

Plot the two curves together and also plot the Errors of Forecast

ALSO COMPARE forecast of levels of CPI with actual CPI -- forecasted level of CPI would be:

ln(CPI(T*+1))=Y(T*+1) - ln(CPI(T*)

CPI(T*+1) = exp(Y(T*+!))/CPI(T*) forecast level

Compare this with actual level. Again plot the two curves together and then plot the forecast errors separately

NOW ITERATE THE process -- move from T*+1 to T*+2. UPDATE estimated values of b0 and c0 by incorporating the extra data point at T*+1, and then carry out exactly the same process as outlined above.

NOTE that graphs would be made at the END of the forecasting process after all the recursive forecasts have been made

ALSO make a graph of the changing estimates of b0 and c0, I want to see how much stability there is in these estimates and how much they fluctuate over time.

Try some varying values of w0 -- especially w0=0 give the USUAL forecast, where the last period error is NOT taken into account.

See if you can find an optimal value of w0 between 0 and 0.5 (optional)

DO THE SAME THING FOR THE TURKISH CPI and M2 data.