# Study Significance of Parameters in Fitted Model

The estimated parameters of the model may be smallsmaller than the expected estimator variance. This may indicate a need to use a simpler or more structured model.

Get a random sample by applying a moving average filter to a white noise signal.

 In[1]:= XBlockRandom[SeedRandom[1]; whiteNoise = RandomFunction[WhiteNoiseProcess[], {0, 10^3}]; data = MovingMap[{0.34, 1}.# &, whiteNoise, 2]]
 Out[1]=

Fit zero mean time series model to data.

 In[2]:= Xtsm = TimeSeriesModelFit[data, IncludeConstantBasis -> False]
 Out[2]=

Show parameter tables, displaying the estimated time series parameters and their standard deviations, as well as the corresponding -test statistics and -value.

 In[3]:= Xtsm["ParameterTable"]
 Out[3]=

The parameter table indicates that autoregressive coefficient is not significantly different from zero. Find the maximum likelihood estimate of the MA(1) model.

 In[4]:= XmaMLE = EstimatedProcess[data, MAProcess[{\[ScriptA]}, \[ScriptV]], ProcessEstimator -> "MaximumLikelihood"]
 Out[4]=

The Akaike information criterion favors the MLE estimated MA(1) model.

 In[5]:= Xcrit = tsm["SelectionCriterion"]; {crit, TimeSeriesModelFit[data, maMLE][crit], tsm[crit]}
 Out[5]=

Compute the 95% confidence interval of the moving-average parameter.

 In[6]:= XTimeSeriesModelFit[data, maMLE]["ParameterConfidenceIntervals", ConfidenceLevel -> 0.95]
 Out[6]=

## Mathematica

Questions? Comments? Contact a Wolfram expert »