# 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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### Estimating an ARMAX model using an I(2) exogenous variable

Is it valid to estimate an ARMAX model using I(1) and I(2) variables, which are made stationary after first and second differencing, respectively? For instance, I have an I(1) stock price variable, ...
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### Is my approach to compute Granger causality valid?

I have two time-series, let us call them A (colored in red) and B (colored in blue). There are ~770 data points per time-series. Note: Both time-series are in fact not the recorded raw signals, but ...
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### Non-stationary time series: what are the advantages of doing analysis in levels instead of differences?

Suppose we want to analyze some non-stationary time series, x(t) and y(t). For simplicity, assume they are I(1). We can analyze them in levels (using cointegration tests) or in differences. What are ...
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### Why the differenced at lag 12 time series of a SARIMA(0,0,0)(0,1,1)_12 model follow the MA(1) pattern with step 12?

I am trying to understand why the ACF of the seasonally differenced series reveals the AR of MA structure of the original series. For example: The following lines creates a SARIMA(0,0,0)(0,1,1)_12 ...
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### Only first differencing the independent variable?

I am trying to study the relationship between income and preferences for redistribution. I have a panel dataset. I can simply the model (1): preferences = alpha + income + e. However, I'm also ...
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### Why does differencing White Noise induce autocorrelation of $-0.5$?

I am curious about the following problem. Let's have a variable given by white noise, $$y_t \sim \operatorname{NID}(0,1).$$ Let's say we difference it, $$\Delta y_t = y_t - y_{t-1}.$$ And now, if we ...
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### Different results when fitting ARIMA model for levels vs ARMA model for first differences in R

In the following code I show that I get different forecasts when fitting an ARIMA(2,1,0) for cumulative sums of a generated AR(2) model vs. fitting an ARMA(2,0) for the AR(2) itself. Can anyone point ...
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### Difference transformation and Stationarization of Moving Average

I have a temperature sensor data, I want to denoise it. The first thing that came to my mind was to take the moving average, it was very smooth but it is still not stationary. If I take the log ...
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### Estimating VAR of differences of potentially cointegrated variables

What are the possible issues, if any, of estimating a standard two-dimensional $VAR(p)$ of $I(0)$ variables that are first differences of $I(1)$ variables whose potential cointegrating relationship ...
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### Intuition behind the first, second, third order differencing. When to use them?

I am working with time series data and out of curiosity took the first, second and third order differences of my data. However, I am not quite sure when they are used? I also wonder about the ...
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### How to choose the order of differencing?

I have a time series that looks like this I was asked to display the autocorrelation function and perform ADF test and based on that suggest a d for further analysis. I get plots like this and can ...
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### Auto arima capital D

I've got time series 3 years long, there is seasonal uplift during December - but it's not so clear. Seasonal test fails. I train model twice without setting any parameter: ...
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### Role of trend argument compared to integral order in ARIMA model

I am currently studying ARIMA models. When I checked for a Python library to train one, I stumbled upon statsmodels which features ARIMA (and SARIMAX from which ...
1 vote
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### Specifying parameters for SARIMAX model with significant ACF / PACF at tails

I have hourly data that has a period of 1 day or 24 hours / time steps and I hope to do short term forecasting for a few days in advance. The ACF of the raw time series was periodic (see last figure) ...
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### How to interpret those ACF & PACF?

I have some problems when analyzing my time series dataset. Basically, the dataset is about the daily sales volume of an FMCG company (they work from Monday to Saturday with Sunday being a day off, so ...
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### ADF & KPSS Test Reporting Series as I(19)

I am currently attempting to determine the order of integration for a nonstationary time series of the Federal Funds Rate (https://fred.stlouisfed.org/series/FEDFUNDS - Monthly, 1990 to 2004, 168 obs.)...
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### Differencing and Stationarity in Panel Data Analysis

As far as I know, the source of randomness is different in cross-sectional and time-series analysis. The following is my understanding. When we use a cross-sectional data set $\{X_i\}_{i=1}^{N}$, the ...
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### Applying differencing for time series data before regression analysis

I am new to time series regression. I am trying to understand the effect of differencing the time-dependent data before applying regression analysis. I tried fitting lots of regression models but in ...
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### Gradient vs differences to remove non-stationarity in time series?

When dealing with non-stationary time series (for instance, in auto-correlation analysis), differencing (computing absolute differences between consecutive samples/observations) is often regarded as ...
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### SARIMA model selection for my data

I am new to time series analysis. I need to determine whether my series is seasonal or not, and if it requires differencing for building an ARIMA model if it is possible? The time series data is ...
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### If $X_t$ is an AR(2) process, what is $Y_t := X_t - X_{t-1}$?

Q: If $X_t$ is an AR(2) process, what is $Y_t := X_t - X_{t-1}$? Attempted solution: $X_t = \phi_1 X_{t-1} + \phi_2 X_{t-2} + W_t$, where $W_t$ is white noise. \begin{split} Y_t &:...
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### What happens if you difference a IMA?

When we over-difference a time serie, we are introducing units roots in its moving average component, hence obtaining an IMA. My question is: IMA is an integrated time serie, hence it has unit root ...
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### Can I transform variables to comply with conditions on order of integration in an ARDL model?

If log variable have a unit root, can you then difference it? For ARDL model variables should not be I(2) or more. Variables of log form are I(2). Would it be a problem to difference it. What I am ...
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### First difference of logs of negative numbers causes trouble

I have the following problem: I have a timeseries with the prices for a few futures, which is non-stationary (according to ADF test). If I apply first difference of logs, ADF shows stationarity. But I ...
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### Direct multi-step forecasting an integrated time series from a stationary model

I am new to time series analysis. But I am well versed in data science and machine learning. One thing that confused me was modeling the data. For example, I want to create an LSTM or regression model,...
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### ARDL Unit root df

When applying ARDL I used Dickey-Fuller unit root test, and found variables integrated at I(1) and I(0). For running the ARDL model do I use my original data (not differenced) or do I use the ...
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### Interpretation of DCC-GARCH model

For my Master thesis I have to perform the DCC-GARCH model to examine the correlation between real estate house prices and the stock market. I tested the data for normality (both not normal) and ...
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### What's the 'right' number of parameters for an ARIMA model?

I'm working on an unassessed course problem, The file Pas-mile.txt contains the monthly numbers of passenger miles travelled on US airlines for each month between ...
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### Modelling temperature: seasonality, stationarity, differencing

I have temperature-related time daily time series. I plot the time series and found that the plot have seasonal variations. Thus I differenced the series. When I did Dickey-Fuller test for both ...
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### How to generate quantile forecasts from first differences?

Let's say I have a time series and I am taking the first differences and training a model to output the predicted 95% quantiles of these first differences at future time horizons. If this was just a ...
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### ARIMA D coefficient for seasonality lesser than frequency

Lets suppose we have a time series with monthly data (frequency=12) my_tS <- ts(my_monthly_data, start=c(2002,1), frequency=12) When I plot it, I can see a ...
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### Differencing Long Memory Time Series

I came accross some articles stating that differencing a long memory time series leads to memory loss. I don't know much about long-memory time series, but I know how $ARMA$ and $ARIMA$ processes work....
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### How to choose model parameters based on ACF and PACF in SARIMA model?

I have some monthly data which show the number of visitors to a country whose plot is given below Since there seems a non-constant variance, I took the log, which stabilized the variance. To remove ...
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### Is the first difference of a strongly stationary process stationary?

Let $X_t$ be a strongly stationary time series. Is the first-order difference process $\nabla X_t$ always stationary?
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### Linear regression with ARIMA errors and seasonal dummy covariates: how does differencing works?

To model my daily time-series data, I want to use linear regression with ARIMA errors. I also want to introduce several seasonal dummy covariates (day of the week, month of the year). I read in ...
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### AR Modelling. Box Cox and Differencing don't give Stationary Data

I am trying to fit an AR/ARIMA model on electricity data on hourly prices during a almost three year period, I am following the guidelines in Hyndman, R.J., & Athanasopoulos, G. (2018) to do this. ...
1 vote
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### How to calculate the forecast interval for time series prediction obtained by doing seasonal differencing before fitting arima

Here is the link of my previous question. How to forecast a time series which is generated by accumulating data of every five minutes and reset to 0 by the end of the day I am working with a seasonal ...
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### Why Python does not seem to correctly report fitted values in statmodels ARIMA when differencing is involved?

When fitting an ARIMA model using the statsmodels python implementation I see the following behaviour, python does not seem to correctly provide the values for the differenced lags. I am comparing the ...
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### Fit an autoregressive model on a heteroscedastic time-series

I have a time-series that I want to model using an autoregressive process using statsmodel for benchmarking purposes. This time-series is not stationary: visual ...
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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 ...