This paper addresses the problem of fitting a known density to the marginal error density of a stationary long memory moving average process when its mean is known and unknown. In the case of unknown mean, when mean is estimated by the sample mean, the first order difference between the residual...

This paper discusses some tests of lack-of-fit of a parametric regression model when errors form a long memory moving average process with the long memory parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$0d1/2$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>0</mn> <mo></mo> <mi>d</mi> <mo></mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </math> </EquationSource> </InlineEquation>, and when design is non-random and uniform on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$[0,1]$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </math> </EquationSource> </InlineEquation>. These tests are based on...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>