|What is the dimension of my response variable?|
The conditional mean and variance models, regression
models with ARIMA errors, and Bayesian linear regression models in
this toolbox are for modeling univariate, discrete-time data.
Separate models are available for multivariate, discrete-time
data, such as VAR and VEC models.
State-space models support univariate or multivariate
|Is my time series stationary?|
Stationarity tests are available. If your data is
not stationary, consider transforming your data. Stationarity is the
foundation of many time series models.
Or, consider using a nonstationary ARIMA model if
there is evidence of a unit root in your data.
|Does my time series have a unit root?|
Unit root tests are available. Evidence in favor of
a unit root suggests your data is difference stationary.
You can difference a series with a unit root until
it is stationary, or model it using a nonstationary ARIMA model.
|How can I handle seasonal effects?|
You can deseasonalize (seasonally adjust) your data.
Use seasonal filters or regression models to estimate the seasonal
Seasonal ARIMA models use seasonal differencing to
remove seasonal effects. You can also include seasonal lags to model
seasonal autocorrelation (both additively and multiplicatively).
|Is my data autocorrelated?|
Sample autocorrelation and partial autocorrelation
functions help identify autocorrelation.
Conduct a Ljung-Box Q-test to test autocorrelations
at several lags jointly.
If autocorrelation is present, consider using a conditional
For regression models with autocorrelated errors,
consider using FGLS or HAC estimators. If the error model structure
is an ARIMA model, consider using a regression model with ARIMA errors.
|What if my data is heteroscedastic (exhibits volatility clustering)?|
Looking for autocorrelation in the squared residual
series is one way to detect conditional heteroscedasticity.
Engle’s ARCH test evaluates evidence against
the null of independent innovations in favor of an ARCH model alternative.
To model conditional heteroscedasticity, consider
using a conditional variance model.
For regression models that exhibit heteroscedastic
errors, consider using FGLS or HAC estimators.
|Is there an alternative to a Gaussian innovation distribution
for leptokurtic data?|
You can use a Student’s t distribution
to model fatter tails than a Gaussian distribution (excess kurtosis).
You can specify a t innovation
distribution for all conditional mean and variance models, and ARIMA
error models in Econometrics
You can estimate the degrees of freedom of the t distribution
along with other model parameters.
|How do I decide between several model fits?|
You can compare nested models using misspecification
tests, such as the likelihood ratio test, Wald’s test, or Lagrange
Information criteria, such as AIC or BIC, compare
model fit with a penalty for complexity.
|Do I have two or more time series that are cointegrated?|
The Johansen and Engle-Granger cointegration tests
assess evidence of cointegration.
Consider using the VEC model for modeling multivariate,
Also consider cointegration when regressing time series.
If present, it can introduce spurious regression effects.
|What if I want to include predictor variables?|
ARIMAX, VARX, regression models with ARIMA errors,
and Bayesian linear regression models are available in this toolbox.
State-space models support predictor data.
|What if I want to implement regression, but the classical linear
model assumptions might not apply?|
Regression models with ARIMA errors are available
in this toolbox.
Regress robustly using FGLS or HAC estimators.
Use Bayesian linear regression.
For a series of examples on time series regression
techniques that illustrate common principles and tasks in time series
regression modeling, see Econometrics
For more regression options, see Statistics and Machine
Learning Toolbox™ documentation.
|How do use the Kalman filter to analyze several unobservable,
linear, stochastic time series and several, observable, linear, stochastic
functions of them?|
Standard, linear state-space modeling is available in