Expected Value and Auto Covariance for Moving Average Process with Lag h=s-t

In summary, a Moving Average Process is a statistical model used to understand the pattern or trend of a time series data by smoothing out random fluctuations. It is calculated by taking the average of a specified number of data points over a time period and moving the window of data points forward. The purpose of using a Moving Average Process is to identify underlying patterns and make predictions about future data points. However, it has limitations in capturing nonlinear data patterns and may not accurately represent sudden changes. It is also different from a Simple Average as it considers a specified time period and is better at identifying trends over time.
  • #1
GottaLoveMath
3
0

Homework Statement


Y_t = u_(t-1) + u_(t) + u_(t+1) where u~WN(0,sigma^2)

Find expected value, and auto covariance as a function of lag h = s-t for some s and t

Homework Equations

The Attempt at a Solution



so E(y) = 0

cov(Y_t, Y_h) = cov(u_(t-1) + u_(t) + u_(s-t+1), u_(s-t-1) + u_(t) + u_(s-t+1)

Is this set up correctly, it only really works for s = 2t or something weird like that. [/B]
 
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  • #2
What is the covariance if h=0?
How about h=1?
It looks like it should decrease as h increases.
 

Related to Expected Value and Auto Covariance for Moving Average Process with Lag h=s-t

What is a Moving Average Process?

A Moving Average Process is a statistical model used to understand the pattern or trend of a time series data. It is a technique that helps to smooth out random fluctuations in data and identify underlying patterns or trends.

How is a Moving Average Process calculated?

A Moving Average Process is calculated by taking the average of a specified number of data points over a time period, and moving the window of data points forward one at a time. This creates a new average for each point in time, resulting in a smooth line that represents the overall trend of the data.

What is the purpose of using a Moving Average Process?

The purpose of using a Moving Average Process is to identify and understand the underlying pattern or trend of a time series data. It helps to remove random fluctuations and anomalies, making it easier to see the overall trend and make predictions about future data points.

What are the limitations of a Moving Average Process?

One limitation of a Moving Average Process is that it can only capture linear trends and may not be suitable for nonlinear or complex data patterns. Additionally, it can smooth out important data points and may not accurately represent sudden changes or outliers in the data.

How is a Moving Average Process different from a Simple Average?

A Moving Average Process takes into account a specified number of data points over a time period, while a Simple Average only considers the data points at a specific point in time. This means that a Moving Average Process is better at smoothing out fluctuations and identifying trends over time.

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