# Questions tagged [stationarity]

A strictly stationary process (or time series) is one whose joint distribution is constant over time shifts. A weakly stationary (or covariance stationary) process or series is one whose mean and covariance function (variance and autocorrelation function) do not change over time.

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### Is it fine to choose 0 lag for adf test in my data?

The level values weren't stationary so I took percent changes $(P_t-P_{t-1})/P_{t-1}$. Here's the data: These are the PACFs to determine lags. I think the lag can be 0, or 7 or 11 in case of GDP and ...
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### Interpreting ACF and PACF plots on trading volume

I'm a fairly new one to time series analysis. I was analyzing the daily trading volume of stock derivatives for the past year and trying to see if there is a seasonality pattern. I tried to make the ...
2answers
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### Making an AR(3) model weakly stationary

I have a model as:$$r_t=0.05+\frac{7}{6}r_{t-1}+\frac{1}{6}r_{t-2}-\frac{1}{3}r_{t-3}+a_t$$ When checking for stationarity: $$1-\frac{7}{6}x-\frac{1}{6}x^2+\frac{1}{3}x^3=0$$ I get $x\in \{-2,1,1.5\}$....
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### Non stationarity and forecasting

Let's assume we have estimated a linear regression model on a dataset from 2000 to 2017. The data were stationary. What happens if the data are no longer stationary in the next years? Do the forecasts ...
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### How to interpret regression results when the data have been detrended?

I am planning to build a linear regression model where I explain flight ticket demand with airfares, lagged airfares, GDP etc. based on monthly data from the past 15 years. This is my first time ...
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### Do Recurrent Neural Networks assume stationarity or just a general kind of sequential dependence?

Just when I thought I had convinced myself that RNNs make no other assumption about a sequence other than that there are dependencies between the inputs and that (in the case of monodirectional RNNs) ...
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### Normality of tau-statistics ($\tau_{\mu}$ and $\tau_{\tau}$) in presence of unit roots

The original Dickey-Fuller (1979) paper, considers three regressions ($(1.1), (2.1)$ and $(2.2)$) but only two DGP ($1.1$ and $2.1$), while deriving the limiting distributions. The paper defines three ...
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### Autocorrelation AR(1) process

I am doing a self-study question. I need to find the autocorrelation $\rho(2)$ for the following AR(1) process: $y_t = y_{t-1} + \epsilon_t;\\ \epsilon_t \sim (0,\sigma_\epsilon^2)$ For that I need ...
0answers
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### HAC variance to construct standard errors

I am facing some difficulties understanding this question. It hasn't been long since I started with econometrics, so I'm new to all of this. Suppose we have a function E[c_t|y_t,c_{t-1},y_{t-1},c_{t-...
1answer
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### Recognizing the Seasonal Effects from a Time Plot

From the first plot, I have determined that there is a seasonal pattern of period $L = 12$. However, in my ACF plot (a), it appears that the period is $L = 6$. Am I misinterpreting? The data had a ...
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### Second-order and strictly stationary time series is weakly stationary - proof

I keep reading that second-order and strictly stationary time series has constant mean, variance and its autocovariance is time independent, but I can't find proof of that. My definition of such time ...
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### What are the characteristics of a trend and break stationary process?

I have a time series with around 380 data points (day-wise data acquired from instruments). I want to model these in ARIMA. It is my understanding that first I'll have to check for stationarity of the ...
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### Is AR timeseries always invertible?

I have just started learning time-series and the foremost thing that I read was that in my book it is explicitly written that an AR process is always invertible. But why is that ? If XT= a X(T-1) + et ...
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### Interpretation of several I(1) variables ADL regression

I see a lot of weird interpretation of coefficients, when working with a time-series model with two (or more) variables. Specifically I am thinking of two series that are I(1) and are then log-diffed ...
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### Time Series Stationary or Not

Here is my time series plot of some data. There appears to be a constant variance, but I don't believe that the mean is constant (e.g., big dip around time $t=17$ and big increase around time $t = 57$)...