Questions tagged [differencing]

Differencing is a time series transformation used for removing unit roots. It can be simple or seasonal (for seasonal unit roots), first-order or higher-order (for multiple unit roots), also fractional order. Do NOT confuse with tag *differences*

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How $\psi_{j}$ weights of the AR(p) process satisfy the difference equation?

The parameters $\phi_{1}, \phi_{2}, \ldots, \phi_{p}$ of an AR(p) process $$ z_{t} = \phi_{1} z_{t-1} + \cdots + \phi_{p} z_{t-p} + a_{t} $$ or $$ (1-\phi_{1}B-\cdots-B^{p}) z_{t} = \phi(B) z_{t} = ...
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Show that if $x_t$ is a stationary time series then $\Delta x_t$ is also (weakly) stationary

I need to express $E[\Delta x_{t}]$ and $\gamma_{\Delta X}(h)$ in terms of $E[x_{t}]$ and $\gamma_{X}(h)$. The first part of this is trivial and can easily be shown that $E[\Delta x_{t}] = \mu_{X} - \...
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How do I turn the n-ahead ARIMA predictions to undifferenced values?

I`m doing a Monthly sales forecast based on some historical data. My question is when I do the Arima(p,d,q) and then I do forecast(arima_model) in order to get the fitted values, which are nicely ...
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How to invert differencing in time series data if I am making multiple steps prediction?

I have a time-series that I would like to use for predicting 36 timesteps in advance using LSTM. It is not stationary so I differenced the series by subtracting each point from the next one. My ...
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Should I difference my data before run a ADF test?

I plot my data as shown in the following screenshot: Clearly the series contains a trend. A first order difference of my data will eliminate the trend, which I plot as follows: Now I would like to ...
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Is the variance of the process in first differences larger than the variance of the undifferenced series?

I have a question regarding a a sinlge-choice problem in my time series course. My question is the following: Is the variance of a process in first differences larger than the variance of the ...
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How to get rid of non-stationarity with panel data?

I've read that one can eliminate non-stationarity by differencing the data one has collected. What does this mean exactly in a panel data context? I've only found examples for cross-sectional data but ...
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Intuition: Differencing Removes Long-run Effects

Consider typical differencing methods discussed in statistics. First differencing De-meaning My question is: (in the context of time-series) What is an intuitive way to understand that differencing ...
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ARIMA - GARCH or AR-GARCH

I am looking at equity returns and they are not stationary at level. So i take the 1st difference to make them stationary. My GARCH(1,1) model is modeled using an AR(1) parsimonious model. But, since ...
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Conflicting ACF/PACF after first-difference

I have yearly data. When I do a Dickey-Fuller test it gives me insignificant results, indicating that the series are non-stationary. After differencing them the DFT tells me they are now significant ...
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Serial correlation fix

I have some question about positive serial correlation: What happens to the standard error of the model once transformed using generalized differencing/Cochrane-Orcutt? Is it higher than the original ...
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In SARIMA model do we start by first differences or seasonal differences?

I don't know the general formula for SARIMA model for additive and multiplicative model. I don't know whether we start by first differences or seasonal differences. I only know the formula of ...
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Regression of a time series difference

Suppose $x(t)$ and $y(t)$ are two time series. I regress $y(t)$ against $x(t)$, and obtain $$y(t)=ax(t)+b+z(t) $$ for some regression constants $a, b$ and residue $z(t)$. Define $\Delta u(t):=u(t+1)-u(...
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Unsure If I should do a seasonal difference in my dataset

I'm doing my final project for my bachelor's on Time Series, I'm using a dataset for precipitation for São Paulo City here in Brazil. My goal is to divide the dataset into training and testing and ...
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What happens if one of my series in the VAR is not stationary?

I have a VAR model that comprehends 6 series. Only one of them is non-stationary even after taking the 1st difference. Do I need to take the 2nd difference? My concern is to approximate too much the ...
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Interpreting Impulse Response Function after first differences of logarithm transformation

I created an impulse response function from a VAR model. I used data transformed by taking the first difference of logarithms. I am now in trouble with giving a substantive interpretation of the scale ...
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Differencing my training set data

I'm trying to difference the non-stationary data in my training set with ndiff() and nsdiff(), but R returns the following: Warning: The chosen seasonal unit root test encountered an error when ...
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How to make quarterly population data stationary?

So, I am trying to build the Time Series model for the quarterly population estimate for Ontario provided by Stats Canada (https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=1710000901). As seen ...
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Formal way to test what kind of differencing is necessary?

I'm working on a project that concerns time series data for South-Africa. My series has 34 explanatory variables and only (!) 30 yearly observations. The analysis is meant to be high-dimensional, ...
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How to inverse difference time series data?

I'm preparing a time series model with LSTM, I noticed that the time series data is not stationary so I used diff(period=1) in ...
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In a time series forecasting, should we apply differencing on entire dataset if one or two features are non stationary?

I'm working on a time series forecasting model using VAR (Vector Autoregression). I have 6 features, out of which 2 features are not stationary. If I apply first-order differencing on those features, ...
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Evaluation of trend removal methods

Let's assume the following time series model where mt is a deterministic trend and Yt is a random noise component: Xt = mt + Yt According to my understanding a trend removal method is considered to ...
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Can second order differences stationary series be estimated via VECM model without considering support from economic theory?

Because some series contain negative raw data, and data is normalized by MinMax. Can VECM be used after second-order difference where the series are stationary? If can, whether the number of lagged ...
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Expectation of a first difference of I(1) stationary?

I have a simply but still challenging question (at least to me). My question boils down to the following, if the first differences $\Delta y_t$ of an I(1) process is stationary, is then also the ...
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Why is my AR forecast better than my ARIMA forecast even though data is I(1)

I am trying to build a time series model for forecasting. The time plot of the data is as shown Evidently, there is a trend component and the series is not stationary. As the interest is in ...
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Is this an expected behavior of an ARIMA(0,0,4,1,1,1)

I have data of daily sales and want to make a forecast in SPSS modeler, however I'm getting a result that I can't explain. The plot is inserted below. The fit is the red line and the blue is the ...
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Is HEGY or CH test better in a small sample (40 monthly observations)?

I have a time series of monthly data that is 40 observations ($3\frac{1}{3}$ seasonal cycles) long. HEGY test and CH test give contradicting results w.r.t. presence of a seasonal unit root. HEGY test ...
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How to fit VAR after differencing (Error:NA in y)?

I want to run VAR model by using vars::VAR. Since my X1 was not stationary, I differenced it by diff(data$X1), then got a data ...
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SARIMA without seasonal differencing

I am trying to forecast daily data with (S)ARIMA, having observations for the last 180 days. STL decomposition clearly shows seasonality and ACF plot shows spikes at 7, 14, 21, etc. days so that I ...
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Time series rejects the null hypothesis for ADF test with drift no trend. Is the time series stationary? Must I differentiate?

TL;DR: My time series passes a ADF test with drift no trend. So, should I leave my data alone and proceed? Or do still need to differentiate it before modelling, because it has drift? Or have I made ...
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Differencing data with missing values?

I have a non-stationary dataset that I would like to model using a VAR model. I need to difference it to make it stationary, however my dataset contains a lot of NaN's at random points, so using ...
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Fail to decompose and make stationary time series

I am looking for some suggestions for my time series. I am dealing with the column "Temperature (C)" from this dataset. I am trying to make it stationary in order to do some forecasting on ...
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Is the correlation coefficient for first differences an estimate of the correlation between the two DGPs in levels?

I think not, because the series in levels is dependent on time and that’s not what we are interested in, but I’m a bit lost here. An additional thought - I know the beta coefficient we get when ...
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Order of integration of a time series process

I am having trouble solving the order of integration of a time series process. Consider the following processes: \begin{align*} \epsilon_t &\sim i.i.d.(0,1) \\ x_t &= \alpha x_{t-1}+\epsilon_t ...
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For purely descriptive purposes, is it okay to run correlations between two non stationary series?

I have been obsessed with trying to conduct an analysis in the “correct” way. I read that no time series analysis should be conducted on non stationary series. I found both my series have a unit root ...
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If two first differenced times series are white noise, then what’s the point in finding relationships?

If x’ and y’ are two first differenced time series, I’ve see many analyses where people find a model where y’ is predicted using x’ in some way (lagged or not). If both x’ and y’ are stationary with ...
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Can I use all estimates in a first differenced regression to apply to levels?

I have a time series y where I took the first differences, y’, and an independent variable x where I also took the first differences to get x’. When I run a regression between y’ and independent ...
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Don’t use first differences if you expect lagged effects?

I’m interested in seeing if two first differenced variables are cross correlated with one another (the original data are non stationary, hence I use the first differences which I show with a DF test ...
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Problem with ets function diagnostic for model with trend and seasonality

I have been meaning to fit an exponential smoothing model to a monthly series that looks like the one below: When I decompose the series it is almost evident that we have seasonality and also there ...
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SARIMA: Determining the integration number

i am working with a time series that after calculating the first difference, it remains non-stationary. When plotting the series I see there is some seasonality at half and end of year. I would like ...
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What does this autocorrelation plot show?

I'm working with this dataset from Forecasting: Principles and Practice 2nd Edition. I've calculated the 12-month seasonal difference (middle) and the autocorrelation plot (right). The ...
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Which of these differenced datasets is stationary?

I'm working with this dataset from Forecasting: Principles and Practice 2nd Edition. It is clearly not stationary due to the seasonal component. I have performed 3-month, 9-month, and 12-month ...
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Removing trend and seasonality does not seem to result in a stationary time series?

I have some sales data, that I want to do time series analysis on. On the plot there are clear trend and seasonality visible. To test whether a series is stationary I have created a function that ...
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Differencing data for square root data

Let $Y_t$ follows ARIMA(1,1,1) and $\Delta(Y_t)=Y_t - Y_{t-1}$. If $\Delta(\sqrt{Y_t})=\sqrt{Y_t}-\sqrt{Y_{t-1}}$ then $\sqrt{Y_t}$ follows ?
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Why difference a time series for forecasting?

From various econometrics/time series analysis/forecasting texts I take that it is common practice to difference time series that have a stochastic trend before modeling them with forecasting models. ...
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Using a VAR model to predict stock prices

I ran into an issue while trying to predict stock prices using a Vector Autoregression (VAR) model. After noticing that all the series are non-stationary (see example below): I took first differences ...
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Differentiating data before exponential smoothing?

I know that to perform exponential smoothing you don't have to make your time series stationary, but I seem to get better results when I do it. Do you know anything about it?
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Testing for multicollinearity: use same specification as main model and clustered standard errors or not

When I am trying to check multiple panel data for multicollinearity by regressing one independent variable on another, should I use exactly the same specification as the main model or is an OLS ...
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Different stationarity of time series

I am testing stationarity of multiple time series so I can run multiple regression later. My results are mixed. The variables that I plan to be my dependent variables are non-stationary at level, by ...
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VAR Model with different integration order

I am trying to create a VAR model with 4 variables. 3 of them need 2 differences in order to be stationary, while 1 needs only 1. When I take differences I loose one row of data, so there is one ...
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