If a simple N-span moving average is applied to a time series that has a linear...

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If a simple N-span moving average is applied to a time series that has a linear trend, say, y, = Bo + Bit + E₁,1 will lag behind the observations. Assume that the observations are uncorrelated and have constant variance. Show that at time T the expected value of the moving average is N-1 E(M₁) =B₁ + B₁T - N=¹₁. - 2 If a simple N-span moving average is applied to a time series that has a linear trend, say, y, = Bo + Bit + E₁,1 will lag behind the observations. Assume that the observations are uncorrelated and have constant variance. Show that at time T the expected value of the moving average is N-1 E(M₁) =B₁ + B₁T - N=¹₁. - 2

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To show that the expected value of the moving average at time t is EM B BT A we can use the followin... View the full answer