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# 统计代写|时间序列分析代写Time-Series Analysis代考|STAT519 What is a stationary time series?

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## 统计代写|时间序列分析代写Time-Series Analysis代考|What is a stationary time series?

Stationary Time Series
Stationary time series models are time series that the mean and the variance of the variable don’t depend on the time. Therefore the mean and variance of a stationary time series are constant. They do not have any periodic fluctuations. A stationary time series is simply a stochastic process with constant mean and variance. There are strong stationary series and weak stationary series.
When the distribution of the time series is same as the lagged time series, then it has a strong form of stationary. When the mean and correlation function of a time series does not change by shift in time it is a weak stationary time series. Auto covariance function is not a function of time.
Stationary series is spread around the mean line in a given range. Below is a graph of a stationary time series. Stationary series spread around the mean line in a given range or given upper and lower limits. It has neither trend nor seasonality.

Non Stationary Time Series
Trend, seasonal, cyclic and random patterned series fall under non stationary series. In order to do predictions on a non stationary series, it should be transformed into a stationary series.

Stochastic Process
Stochastic process is a collection of random variables. Time series with the time variable is a basic type of a stochastic process. It is a model for the analysis. This can also be called as random process
Mean of a stochastic process
$\mu_t=\mathrm{E}\left(y_t\right)$ Where $\mathrm{t}=0, \pm 1, \pm 2 \ldots, \pm \mathrm{n}$
Autocovariance of stochastic process
$y_{t, s}=\operatorname{Cov}\left(y_t, y_s\right)$
$\operatorname{Cov}\left(y_t, y_s\right)=\mathrm{E}\left(y_t-\mu_t\right)\left(y_s-\mu_s\right)$
Where $t, s=0, \pm 1, \pm 2 \ldots, \pm n$

## 统计代写|时间序列分析代写Time-Series Analysis代考|How to make a stationary Time Series Model

When a time series is not stationary, it should be turned into a stationary series before estimating a model. Below four techniques are four methods to that can be used to transform a non stationary variable into a stationary one.

Decomposition technique

Smoothing technique

Differencing technique

Transforming to log technique
2.2.1 Decomposition Techniques
Decomposition models in time series are used to identify and describe trend and seasonal factors.
Decomposition means to break down into simpler parts. When decomposition models are used, we can identify these patterns/factors separately.
Some seasonal patterns of a time series model can be describe as festive season effects, holiday effects. As an example think that there is a festive season effect on sales of a textiles company, the company cannot clearly identify how its sales behave in long term. Therefore we can use this method to remove seasonal effects of the time series data set and then try to identify what kind of a trend, these sales have in long term (do the sales increase or decrease annually?)

## 统计代写|时间序列分析代写Time-Series Analysis代考|What is a stationary time series?

$\mu_t=\mathrm{E}\left(y_t\right)$ 在哪里 $\mathrm{t}=0, \pm 1, \pm 2 \ldots, \pm \mathrm{n}$

$y_{t, s}=\operatorname{Cov}\left(y_t, y_s\right)$
$\operatorname{Cov}\left(y_t, y_s\right)=\mathrm{E}\left(y_t-\mu_t\right)\left(y_s-\mu_s\right)$

## 统计代写|时间序列分析代写Time-Series Analysis代考|How to make a stationary Time Series Model

$2.2 .1$ 分解技术

## MATLAB代写

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