# Nowcast this

Nowcasting is a technique which has recently gained popularity in economics. Essentially low frequency economic variables are foretasted by a series of higher frequency variables in state space. The canonical example is that of predicting GDP figures (low frequency of data release) from higher frequency variables such as jobless figures, industrial orders and trade balance.

Such a model can be written as a system of two equations:

measurement equations linking observed series to latent variable (or state process)

\[Y_t^{K_Y} = \mu + \zeta(\Theta)X_t + G_t\]transistion equations describing the state process dynamics

\[X_t = \phi(\Theta)X_{t-1} + H_t\]

where in the above equations \(Y_t^{K_Y}\) is the vector of observed variables and \(X_t\) is the unobserved state variables, the dynamics of which are explained by the transition equation.

\(G_t\) and \(H_t\) represent covariance matrices of the disturbances and \(\phi(\Theta)\) and \(\zeta(\Theta)\) represent matrices of the coefficients. The covariance matrices are determined from an iterative Expectation-Maiximisation algorithm.

As the model is in state-space we can now gain projections for both the observed and the predicted variables using the Kalman filter, as well as allowing us to have missing variables in our series.

It’s an interesting approach as the forecast for the low-frequency variable gets progressively more accurate as more data is released as we move closer to the announcement date. This means that there is a news component or “unexpected” component which we obtain from the model as the long-term (or indeed short-term) variables have their forecast updated, which is could be a useful signal.

A paper by Marta Bańbura, Domenico Giannone, Michele Modugno and Lucrezia Reichlin reviewing the approaches can be found on the ECB website.