# What does variance decomposition show?

## What does variance decomposition show?

The variance decomposition indicates the amount of information each variable contributes to the other variables in the autoregression. It determines how much of the forecast error variance of each of the variables can be explained by exogenous shocks to the other variables.

**What is impulse response VAR?**

An impulse-response function describes the evolution of the variable of interest along a. specified time horizon after a shock in a given moment.

### How do you calculate forecast error variance?

et(l) = Yt+l − ˆYt(l) = µt+l + Xt+l − µt+l = Xt+l, so that E[et(l)] = E[Xt+l] = 0. ▶ Thus the forecast is unbiased. ▶ And the forecast error variance is var[et(l)] = var[Xt+l] = γ0, which does not depend on the lead time l.

**What is generalized variance decomposition?**

The generalized forecast error variance decomposition shows to what extent return variability in one currency market can be explained by the innovations from other markets in the VAR system.

#### How do you interpret VAR impulse response?

Usually, the impulse response functions are interpreted as something like “a one standard deviation shock to x causes significant increases (decreases) in y for m periods (determined by the length of period for which the SE bands are above 0 or below 0 in case of decrease) after which the effect dissipates.

**How do you perform a VAR analysis?**

The procedure to build a VAR model involves the following steps:

- Analyze the time series characteristics.
- Test for causation amongst the time series.
- Test for stationarity.
- Transform the series to make it stationary, if needed.
- Find optimal order (p)
- Prepare training and test datasets.
- Train the model.

## When would you use a VAR model?

A Vector autoregressive (VAR) model is useful when one is interested in predicting multiple time series variables using a single model.

**How do you calculate impulse response VAR?**

The impulse response is the derivative with respect to the shocks. So the impulse response at horizon h of the variables to an exogenous shock to variable j is ∂yt+h∂ϵj,t=∂∂ϵj,t(Πyt+h−1+ϵt+h−1)=⋯=∂∂ϵj,t(Πh+1yt+h∑i=0Πiϵt+h−i).

### What is Anova decomposition?

Analysis of variance (ANOVA) is a statistical procedure for summarizing a classical linear model—a decomposition of sum of squares into a component for each source of variation in the model—along with an associated test (the F-test) of the hypothesis that any given source of variation in the model is zero.