Time Series Analysis Flashcards
A time series
set of observations for a variable over time
time series model
captures the time-series pattern and allows us to make predictions about the variable in the future.
primary limitation of trend models
not useful if the residuals exhibit serial correlation.
autoregressive model (AR)
dependent variable is regressed against one or more lagged values of itself
dependent variable is regressed against one or more lagged values of itself
time series being modeled is covariance stationary
A time series is covariance stationary if it satisfies the following three conditions:
1- Constant and finite expected value.
2- Constant and finite variance.
3- Constant and finite covariance
one-period-ahead forecast for an AR(1) model
xt+1=b0+b1xt
two-step-ahead forecast for an AR(1) model
xt+2=b0+b1xt+1
When an AR model is correctly specified, the residual terms
will not exhibit serial correlation
Serial correlation (or autocorrelation) means the error terms
positively or negatively correlated.
When the error terms are correlated
standard errors are unreliable and t-tests can incorrectly show statistical significance or insignificance.
mean reversion
tendency to move toward its mean
mean reversion formula
xt=b0(1−b1)
root mean squared error(RMSE)
accuracy of autoregressive models in forecasting out-of-sample values
lower RMSE for the out-of-sample data
lower forecast error and will be expected to have better predictive power in the future.