Time series understanding a proposition

In summary, the conversation discusses a proposition regarding the non-singularity of a covariance matrix for a stationary process. The speaker wants to find a counter example to prove that the converse of the proposition is not true. They mention a white noise process as a possible counter example, but are unsure of how to construct it. They ask for assistance in constructing the counter example.
  • #1
nikki92
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Homework Statement



Proposition: If C(0)>0 and C(h)->0 as h-> infinity, then the covariance matrix gamma_n =[c(i-j)] for i,j- 1,2,...n of (x_!,...x_x)' is non singular for every n.

I want to convince myself that the converse is not true. (ie I want a counter example of a stationary process {x_t} such that Ganna_n is nonsingular for all n and c(h)-/->0 as h->infinity

Homework Equations





The Attempt at a Solution


I am not sure how to construct such a counter example.
 
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  • #2
I have read that a white noise process yields such a counter example, but I am not sure how to construct this. Any help would be appreciated.
 

1. What is a time series?

A time series is a set of data points collected at regular intervals over time. It represents the changes or trends in a variable or phenomenon over a period of time.

2. What is the importance of understanding a time series?

Understanding a time series is important because it allows us to identify patterns, trends, and relationships in the data. This can help us make predictions and inform decision-making in various fields such as economics, finance, and weather forecasting.

3. What are the components of a time series?

The components of a time series include trend, seasonality, cyclicality, and irregularity. Trend refers to the long-term pattern or direction of the data. Seasonality refers to regular patterns that occur at fixed intervals. Cyclicality refers to patterns that occur at irregular intervals. Irregularity refers to random fluctuations or noise in the data.

4. How do you analyze a time series?

There are various techniques for analyzing a time series, including statistical methods such as moving averages, exponential smoothing, and autoregressive integrated moving average (ARIMA) models. Visualizations such as line graphs and box plots can also help in understanding the data.

5. What are some common uses of time series analysis?

Some common uses of time series analysis include forecasting future values, identifying trends and patterns, detecting anomalies or outliers, and making informed decisions in various industries such as finance, marketing, and healthcare.

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