Macroeconomic Forecasting
12-09-2026
Learn how to choose between forecasts from competing models or sources
Learn how to assign a number to forecast performance using various “summary” statistics
If you have to forecast, forecast often.
Forecast from the same model need to be repeated.
The properties of a forecaster/model (correct on average, low volatility) are evaluated using various statistical measures
Forecasters/models are evaluated using out-of-sample forecast performance
There are many dimensions/statistics one could use
Evaluation has to be repeated
It is often said there are two types of forecasts… Lucky or Wrong !
Economic variables are random processes and therefore each has a probability distribution.
We call that distribution, which is typically unknown, the data generation process (DGP) of that variable
If the variable can have continuous values, the probability of a single point forecast being equal to the eventual outcome is zero
Therefore, it is only possible to attach a probability to a range of possible outcomes encompassing the actual outcome
If a point forecast happens to be equal to the actual outcome, it is purely by chance and quite unlikely to be repeated in the next period
Every economic variable has an underlying *data generating process (GDP)
The DGP is a probability density function, for example, \(N(\mu,\sigma^2)\)
For any sequence of data points, \(\pi_t\) drawn from this distribution, we may write
\(y_{t+1}=E_t(y_{t+1}|Information)+\epsilon_{t+1}\)
Where \(E_t\) is the “condistional expectation operator” and \(\epsilon_t\) is a residual error term, which we expect to have zero mean.
The density for is difficult to estimate precisely, requiring a considerable amount of data in practice
Conditional means can be estimated more readily using a variety of statistical procedures
For example, it is often assumed that the conditional mean is a linear function of other explanatory variables (information set), and to use ordinary least squares to estimate the unknowns in that relationship
Assuming that conditional means is known
\(y_{t+1}=E_t(y_{t+1}|Information)+\epsilon_{t+1}\)
We still need an estimate of \(\epsilon_{t+1}\) to complete the forecast.
Assuming \(\epsilon_{t+1}\) is a white noise process from a normal distribution with zero mean, say, our best guess for of its future values is zero.
So it is typically impossible to predict the actual outcome exactly.
Even if we know the conditional mean, our conditional forecast will necessarily differ from the outcome.
Indeed, the observed forecast errors will obviously reflect the distribution of the true error term, which is normally unknown
It follows that … The best we can hope for is that, on average, our actual forecast errors are zero. Why?
\(y_{t+1}=E_t(y_{t+1}|Information)+\epsilon_{t+1}\)
Recall that with as \(T \rightarrow infinity\),
\(\frac{(\sum_{i=1}^{n}\epsilon_t)}T \rightarrow 0\) in probability.
If you want to be a reputable forecaster
If the forecasting model for the series we are interested in is
\(y{t+1}=F(X_{t+1};\theta)+\epsilon_{t+1}\)
The RHS or explanatory variables \(X_t\), will need to be forecasted using additional equations, namely:
\(X_{t+1}= G(Z_{t+1};\beta)+u_{t+1}\)
\(y{t+1}=F(X_{t+1};\theta)+\epsilon_{t+1}\)
\(y{t+1}=F(X_{t+1};\theta)+\epsilon_{t+1}\)
Economic variables are inherently random
There are unknown parameters in the conditional mean that need to be estimated
Explanatory variables also need to be forecast and could be random quantities themselves
The working form of the conditional mean may be misspecified
How can we measure forecast uncertainty?
How do we use a measure of forecast uncertainty in practice?
Unfortunately, there is no unique measure of forecast accuracy and precision
The smaller they are the better are forecast
Bias: the difference between the forecasts and the correct outcome (on average)
Variance (standard forecast error, SE): A narrow range of outcomes is compatible with the forecast
Mean Squared Forecast Error (MSFE): A combination of bias and variance that is commonly reported in forecast comparisons
The mean square and absolute error assume a symmetric cost associated with positive and negative forecast errors
However, the cost of forecast errors can be symmetric
Examples:
Airplane departure
Inflation forecast for inflation targeting (deflation often perceived more costly than inflation)
Need different criteria for these cases
Often useful to compare these measures against those that are obtained from using a benchmark forecast such as the naive forecast or the consensus forecast ? Our economic/behavioral models should be at least as good forecasters as the established benchmark ? Note, however, that there is often a trade-off between forecasting accuracy and the number of parameters one has to estimate in the economic model ? The advantage of economic models is that enable you to assess the reasons behind any forecast error
Compare the performance of your model agains that obtained using naive (no change) forecasting model:
Assumed 1-step ahead forecast is: \(\hat y_t=y_{t-1}\) \(MAPE_{naive}=100 \frac {1}{f} \sum_{i=1}^{n} |\frac{Y_t - Y_{t-1}}{y_t}|\)
Note that the MAE formula cant be calculated if \(y_t=0\) for any period
It also not not suitable for variables expressed in log form
Objective: see how using rolling forecasting strategy instead of the standard expanding window can improve forecast accuracy ? What if potential structural breaks in the future are possible? - I will use simulated data - For assessment, you will use India GDP growth data and analyze growth slowdown after the global financial crisis
By hand! ? Given: Thailand monthly year-on-year all items CPI inflation data for 2003-2014
\(y_t=\frac {CPI_t-CPI_{t-1}}{CPI_{t-1}}\)
Source: Haver Analytics ? Objective: Evaluate and compare two 1 month ahead forecasts using actual data for 2014 as a test period ? Let?s work in Excel for this exercise
Step 1 ? Calculate observational errors for forecast 1 ? Recall that forecast (observational) error is
\(FE_t=\hat y_t-y_t\)
Forecast error is denoted by \(e_{1t}=f_{1t}-\pi_t\)
