具有不同功能和不同时限的移动平均线 [英] A moving average with different functions and varying time-frames
问题描述
我有8个变量的矩阵时间序列数据，这些变量具有大约2500点(〜10年的星期一至星期五)，并希望在移动平均值"的基础上计算均值，方差，偏度和峰度.
I have a matrix time-series data for 8 variables with about 2500 points (~10 years of mon-fri) and would like to calculate the mean, variance, skewness and kurtosis on a 'moving average' basis.
让我们说frames = [100 252 504 756]-我想每天在每个(时间)框架上计算上述四个函数-因此，对于100天框架，第300天的收益为[mean variance skewness kurtosis]从日期day-201-day300(总共100天)开始...依此类推.
Lets say frames = [100 252 504 756] - I would like calculate the four functions above on over each of the (time-)frames, on a daily basis - so the return for day 300 in the case with 100 day-frame, would be [mean variance skewness kurtosis] from the period day201-day300 (100 days in total)... and so on.
我知道这意味着我将获得一个数组输出，并且第一个frame天数将是NaN，但是我无法弄清楚完成该操作所需的索引...
I know this means I would get an array output, and the the first frame number of days would be NaNs, but I can't figure out the required indexing to get this done...
推荐答案
这是一个有趣的问题，因为我认为最优解的均值不同于其他样本统计信息.
This is an interesting question because I think the optimal solution is different for the mean than it is for the other sample statistics.
我在下面提供了一个仿真示例，您可以进行练习.
I've provided a simulation example below that you can work through.
首先，选择一些任意参数并模拟一些数据:
First, choose some arbitrary parameters and simulate some data:
%#Set some arbitrary parameters
T = 100; N = 5;
WindowLength = 10;
%#Simulate some data
X = randn(T, N);
对于平均值，请使用filter获得移动平均值:
For the mean, use filter to obtain a moving average:
MeanMA = filter(ones(1, WindowLength) / WindowLength, 1, X);
MeanMA(1:WindowLength-1, :) = nan;
我原本以为可以使用conv来解决此问题，如下所示:
I had originally thought to solve this problem using conv as follows:
MeanMA = nan(T, N);
for n = 1:N
MeanMA(WindowLength:T, n) = conv(X(:, n), ones(WindowLength, 1), 'valid');
end
MeanMA = (1/WindowLength) * MeanMA;
但是正如@PhilGoddard在评论中指出的那样，filter方法避免了循环.
But as @PhilGoddard pointed out in the comments, the filter approach avoids the need for the loop.
还请注意，我已选择使输出矩阵中的日期与X中的日期相对应，因此在以后的工作中，您可以对两者使用相同的下标.因此，MeanMA中的第一个WindowLength-1观测值将是nan.
Also note that I've chosen to make the dates in the output matrix correspond to the dates in X so in later work you can use the same subscripts for both. Thus, the first WindowLength-1 observations in MeanMA will be nan.
对于方差，我看不到如何使用filter或conv甚至是运行总和来提高效率，所以我在每次迭代时手动执行计算:
For the variance, I can't see how to use either filter or conv or even a running sum to make things more efficient, so instead I perform the calculation manually at each iteration:
VarianceMA = nan(T, N);
for t = WindowLength:T
VarianceMA(t, :) = var(X(t-WindowLength+1:t, :));
end
通过利用我们已经计算出平均移动平均值的事实，我们可以稍微加快速度.只需将上面的内部循环行替换为:
We could speed things up slightly by exploiting the fact that we have already calculated the mean moving average. Simply replace the within loop line in the above with:
VarianceMA(t, :) = (1/(WindowLength-1)) * sum((bsxfun(@minus, X(t-WindowLength+1:t, :), MeanMA(t, :))).^2);
但是，我怀疑这会带来很大的不同.
However, I doubt this will make much difference.
如果其他人可以看到使用filter或conv的巧妙方法来获取移动窗口方差，我将非常有兴趣看到它.
If anyone else can see a clever way to use filter or conv to get the moving window variance I'd be very interested to see it.
我将偏度和峰度留给OP，因为它们本质上与方差示例相同，但具有适当的功能.
I leave the case of skewness and kurtosis to the OP, since they are essentially just the same as the variance example, but with the appropriate function.
最后一点:如果将上述内容转换为通用函数，则可以传入匿名函数作为参数之一，那么您将拥有一个移动平均值例程，该例程可用于任意选择转换.
A final point: if you were converting the above into a general function, you could pass in an anonymous function as one of the arguments, then you would have a moving average routine that works for arbitrary choice of transformations.
最后一点:对于一系列窗口长度，只需为每个窗口长度循环遍历整个代码块.
Final, final point: For a sequence of window lengths, simply loop over the entire code block for each window length.
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