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Stefan Kohl ♦
Stefan Kohl ♦
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Added MathJax.
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edit approved Apr 13, 2016 at 16:49
jeq
edit approved Apr 13, 2016 at 16:49
jeq
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Imagine we define Y(t+n)=Sum(X(t+1)+.....+X(t+n))$Y(t+n)= X(t+1)+.....+X(t+n)$ where X(i)$X(i)$ is an independent normal (i.e. everyday we remove the starting observation and we add a new one). We have N$n$ consecutive observations of Ys$Ys$. I am trying to find the expected number of changes in the sign in the sequence of Ys$Ys$ as a function of N$n$.

Thanks

Imagine we define Y(t+n)=Sum(X(t+1)+.....+X(t+n)) where X(i) is an independent normal (i.e. everyday we remove the starting observation and we add a new one). We have N consecutive observations of Ys. I am trying to find the expected number of changes in the sign in the sequence of Ys as a function of N.

Thanks

Imagine we define $Y(t+n)= X(t+1)+.....+X(t+n)$ where $X(i)$ is an independent normal (i.e. everyday we remove the starting observation and we add a new one). We have $n$ consecutive observations of $Ys$. I am trying to find the expected number of changes in the sign in the sequence of $Ys$ as a function of $n$.

Thanks

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Dobromir Tzotchev
Dobromir Tzotchev
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Expected number of changes in the sign of a rolling sum of independent normal variables

Imagine we define Y(t+n)=Sum(X(t+1)+.....+X(t+n)) where X(i) is an independent normal (i.e. everyday we remove the starting observation and we add a new one). We have N consecutive observations of Ys. I am trying to find the expected number of changes in the sign in the sequence of Ys as a function of N.

Thanks