- 2 Suppose We Have Data On Money Variable M Expressed In Bds And Consumer Price Index P For Barbados For The Per 1 (44.14 KiB) Viewed 19 times
- 2 Suppose We Have Data On Money Variable M Expressed In Bds And Consumer Price Index P For Barbados For The Per 2 (40.27 KiB) Viewed 19 times
valid. Explain the statement thoroughly.
b) Suppose we fit three models for Inflation: ARMA, Regression
Model and VAR Model for the period 1995.02-1997.12. Results of
model estimations and summary statistics of ex-post forecasts for
the period 1998.01-1998.12 are presented below:
(i) Comment on the ex-post forecast results of the three models/
(Be as explicit as possible).
(ii) What does forecast optimality mean?
(iii) Suppose that it turns out that no ex-post forecast is
optimal, what action do you take?
(iv) Give and explain FOUR (4) sources of forecast errors.
2. Suppose we have data on money variable (m,) expressed in Bds $ and consumer price index (p.) for Barbados for the period 1995.01 - 1998.12. We derive Money Growth as Dm, = (m, -m-1)/m-, and Inflation as Dp, = (p. - P.-P.: a) The regression of Inflation on Money Growth may or may not be valid. Explain the statement thoroughly. 10 marks b) Suppose we fit three models for Inflation: ARMA, Regression Model and VAR Model for the period 1995.02 – 1997.12. Results of model estimations and summary statistics of ex-post forecasts for the period 1998.01 - 1998.12 are presented below: ARMA Model: Table 1: Inflation as an MA(9) Process Variable Coefficient Std. Error t-Statistic Prob. с 0.002495 0.001409 1.771103 0.085800 MA(9) -0.941359 0.043129 -21.82681 0.000000 R-squared 0.446404 Mean dependent var 0.002636 Adjusted R-squared 0.429628 S.D. dependent var 0.014489 S.E. of regression 0.010942 Akaike info criterion -6.136890 Sum squared resid 0.003951 Schwarz criterion -6.048013 Log likelihood 109.3956 F-statistic 26.61026 Durbin-Watson stat 2.119110 Prob(F-statistic) 0.000012
Table 2: Summary Statistics for Barbados MA Ex-Post Inflation Forecasts: Static and Dynamic, 1998.01-1998.12 Dpdy Forecast: Dpsta Actual: Dp (Inflation) Forecast sample: 1998:01 1998:12 Included observations: 12 Root Mean Squared Error 0.002362 Mean Absolute Error 0.001843 Mean Absolute Percentage Error 62.18603 Theil Inequality Coefficient 0.294776 Bias Proportion 0.030320 Variance Proportion 0.000437 Covariance Proportion 0.969243 Note: Dpsta: static forecast; Dpdy: dynamic forecast 0.003375 0.002647 91.98534 0.453561 0.150915 0.167102 0.681983 Regression Model: Table 3: Inflation-Money Growth Regression Results: Barbados, 1995:02-1997:12 Variable Coefficient Std. Error t-Statistic Prob. с 0.003232 0.002605 1.240309 0.2236 Dm -0.033917 0.047716 -0.710810 0.4822 R-squared 0.015080 Mean dependent var 0.002636 Adjusted R-squared -0.014766 S.D. dependent var 0.014489 S.E. of regression 0.014595 Akaike info criterion -5.560764 RSS 0.007030 Schwarz criterion -5.471887 Log likelihood 99.31337 F-statistic 0.505251 Durbin-Watson stat 2.054839 Prob(F-statistic) 0.482196
Table 4: Summary Statistics of Barbados Ex-Post Regression Inflation Forecasts: 1998.01-1998.12 Forecast: DPFREGR Actual: Dp Forecast sample: 1998:01 1998:12 Root Mean Squared Error 0.004229 Mean Absolute Error 0.003521 Mean Absolute Percentage Error 129.2530 Theil Inequality Coefficient 0.570135 Bias Proportion 0.151103 Variance Proportion 0.203688 Covariance Proportion 0.645210
Table 5: Vector Autoregressions Results: Inflation and Money Growth:Barbados, 1995.04-1997.12 t-statistics in a Dp Dm Dp(-1) -0.130644 0.275463 (-0.71416] [0.40796] Dp(-2) 0.041680 -0.887481 [0.24951) (-1.43934] Dm(-1) 0.138506 -0.339937 [ 2.79783] [-1.86038] Dm(-2) 0.077143 -0.401097 [1.41330] (-1.99084) с -1.72E-05 0.029311 (-0.00629) [2.89953) R-squared 0.233655 0.207890 S.E. equation 0.013894 0.051284 F-statistic 2.134261 1.837162 Log likelihood 97.00347 53.90846 Akaike AIC -5.575968 -2.964149 Schwarz SC -5.349224 -2.737406 Determinant Residual Covariance 5.06E-07 Log Likelihood (d.f. adjusted) 145.5419 Akaike Information Criterion -8.214658 Schwarz Criterion -7.761171 Table 6:Summary Statistics for Barbados VAR Ex-Post Inflation Forecasts: Static and Dynamic: Barbados, 1998.01 – 1998.12 Actual: Dp Forecast sample: 1998:01 - 1998:12 Included observations: 12 Forecast: Dpfvastat Dpfvady Root Mean Squared Error 0.006941 0.007002 Mean Absolute Error 0.005257 0.005212 Mean Absolute Percentage Error 183.9659 177.8224 Theil Inequality Coefficient 0.565475 0.566750 Bias Proportion 0.013708 0.012584 Variance Proportion 0.409294 0.418726 Covariance Proportion 0.576998 0.568690 Note: Dpvastat: static forecast; Dpfvady: dynamic forecast
(i) Comment on the ex-post forecast results of the three models. (Be as explicit as possible). 10 marks (ii) What does forecast optimality mean? 10 marks 4 (ii) Suppose that it turns out that no ex-post forecast is optimal, what action do you take? Explain. 10 marks