1- a) Explain weak stationarity assuming Yt is a stochastic time series with these properties: Mean:...

  

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1- a) Explain weak stationarity assuming Yt is a stochastic time series with these properties: Mean: Variance: Covariance: E(YŁ) = ? Var (Yt) = ? Yk= ? where Yk is the covariance (or autocovariance) at lag k. b) Suppose ut is a white noise error term with mean 0 and variance o2. Then the series Yt is said to be a random walk if Yt=Yt-1+ut Now we can write; Y₁=Y₁ + U₁ Y₂=Y₁+U₂ = Yo+U₁+U₂ Y3 = Y₂ + U3 = Y₁ + U₁+U₂+Uz 1 In general, if the process started at some time 0 with a value of Yo, we have Yt=Yo + Σut Therefore, E(Yt) = E(Yo + Zut) = Yo . Why? 1- a) Explain weak stationarity assuming Yt is a stochastic time series with these properties: Mean: Variance: Covariance: E(YŁ) = ? Var (Yt) = ? Yk= ? where Yk is the covariance (or autocovariance) at lag k. b) Suppose ut is a white noise error term with mean 0 and variance o2. Then the series Yt is said to be a random walk if Yt=Yt-1+ut Now we can write; Y₁=Y₁ + U₁ Y₂=Y₁+U₂ = Yo+U₁+U₂ Y3 = Y₂ + U3 = Y₁ + U₁+U₂+Uz 1 In general, if the process started at some time 0 with a value of Yo, we have Yt=Yo + Σut Therefore, E(Yt) = E(Yo + Zut) = Yo . Why?

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a Weak stationarity also known as weak stationarity or weak ergodicity is a property of a stochastic time series where the statistical properties of t... View the full answer