序列相关测试 

生成一个 ARProcess 的随机样本.

In[1]:=

X arData = RandomFunction[ARProcess[{.3, .5, -.2}, 1], {1000}];

估计的相关函数缓慢减小为滞后函数.

In[2]:=

X ListPlot[CorrelationFunction[arData, {20}], Filling -> Axis, PlotRange -> All]

Out[2]=

测试延迟10以下的序列相关.

In[3]:=

X AutocorrelationTest[arData, 10, {"TestDataTable", All}]

Out[3]=

通过测试确定了数据是序列相关的.

In[4]:=

X AutocorrelationTest[arData, 10, {"TestConclusion", All}]

Out[4]=

接下来生成 GARCHProcess 的随机样本.

In[5]:=

X garch = GARCHProcess[.4, {.3, .4}, {.2}]; BlockRandom[SeedRandom["Mathematica 10"]; garchData = RandomFunction[garch, {10^2}, 10^5];]

估计的相关函数的值在非零延迟时很小.

In[6]:=

X ListPlot[CorrelationFunction[garchData, {10}], Filling -> Axis, PlotRange -> All, PlotStyle -> PointSize[Medium]]

Out[6]=

用 AutocorrelationTest 检测最初的路径.

In[7]:=

X AutocorrelationTest[garchData["Path", 1], 10, {"TestDataTable", All}]

Out[7]=

In[8]:=

X AutocorrelationTest[garchData["Path", 1], 10, {"TestConclusion", All}]

Out[8]=

虽然没有序列相关，但是切片非独立.

In[9]:=

X garch0 = garchData["SliceData", 0];

In[10]:=

X slices = Table[garchData["SliceData", k], {k, 1, 4}];

用 Hoeffding’s  独立性测试，检测在零时间切片和之后四个切片间的独立性.

In[11]:=

X DistributeDefinitions[garch0]; LaunchKernels[]; tests = ParallelMap[ IndependenceTest[ garch0, #, {"ShortTestConclusion", "HoeffdingD"}] &, slices];

显示在零时间切片和其他时间的值的散布图和测试结果.

显示完整的 Wolfram 语言输入隐藏输入

In[12]:=

X colors = {RGBColor[0.368417, 0.506779, 0.709798], RGBColor[ 0.880722, 0.611041, 0.142051], RGBColor[ 0.922526, 0.385626, 0.209179], RGBColor[ 0.560181, 0.691569, 0.194885]}; Legended[Grid[ Partition[ Table[ListPlot[Transpose@{garch0, slices[[k]]}, ImageSize -> Small, Ticks -> None, PlotStyle -> colors[[k]], PlotLabel -> Row[{"0 vs ", k}]], {k, 1, 4}], 2, 2]], Placed[SwatchLegend[colors, tests], Right]]

Out[12]=