# 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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### Counterintuitive results modeling ARIMA in differences

I have developed an ARIMA model in differences (externally differentiated, not in the Arima() function of the forecast package) that uses the Unemployment Rate variable as an external regressor. The ...
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### Mean and Variance of a Differenced Time Series

Suppose I am differencing a time series. I decide to try out differencing for $d=1, 2$, and $3$ where $d$ is the order of the differencing (by convention of the R function ...
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### How meaningful are the results when you difference the time series dataset before clustering?

On a certain task where I need to perform K-Means Time Series Clustering with DTW algorithm, I would like to know how credible the results are when performing clustering on the original vs a dataset ...
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### How do I transform first-differenced impulse response functions back into levels?

I am estimating a structural VAR where all my variables are I(1). I took the log differences of each variable and generated the impulse response functions. Is there a way to convert the impulse ...
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### ARIMA Model Differencing

I am new to ARIMA model. Best of my knowledge if series is not stationary then we have to make it stationary. Differencing is one method to make it stationary. My question is if I will applied ...
1answer
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### VAR(p) Model with difflog data

I'm doing a regression analysis with a VAR model in R. My data is price and position data in the commodity market, since i want to find out (Granger) causality between them. I took the difflog for ...
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### ARIMA parameter grid search suggests no differencing

I have 3 time series and I am trying to determine the best parameters for ARIMA models. I have made ADF tests for my datasets and in all 3 cases it suggests that differencing is needed. Adjusted ...
1answer
35 views

### Differencing Time Series

I am trying to remove the trends by differencing this logarithmically transformed time series. It contains two columns about COVID-19 Cases in the United States: one column being the number of cases ...
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### 1st or 2nd order of differencing

I have time series and I want to apply differencing to them. However I am not sure whether I should use 1st or 2nd order differencing. In this website (https://people.duke.edu/~rnau/arimrule.htm) it ...
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### Order of differencing and ACF plots

On this website: https://people.duke.edu/~rnau/arimrule.htm I have found information that if the lag-1 autocorrelation is zero or negative, or the autocorrelations are all small and patternless, then ...
1answer
29 views

### How to remove seasonalization in time series data?

I am new to time-series data. I have a dataset with Year(2013-2018), Month, Mdate (1,2,3,4...31), Day (Monday - Sunday), Time (0-24) and Hourly Counts. I saw two seasonal trends in the dataset. I need ...
1answer
20 views

### Changes in correlation between two variables in VAR model after differencing

I am building a VAR model with two variables. When I used it with non-stationary data with strong trend and seasonality, the correlation between variables was 0.48. ...
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### Determining Order of Integration (Matlab Econometrics Toolbox)

I am attempting to implement a variation of the Granger Causality test described in Dave Giles' blog using the Matlab Econometrics Toolbox and teaching myself about the theory along the way. I've ...
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### How to generate fitted values manually for a seasonal ARIMA model?

I am trying to get the fitted values for a SARIMA model, and I can only access the arima() or auto.arima() functions in 'forecast' package in R for benchmarking my results (which is probably not the ...
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154 views

### Detrended data and ARIMA modeling

What data should I use in ARIMA modeling when I do detrending, is it the original data or the detrended one? Then, what is the d component of the ARIMA model, is it d=0 or d=1?
1answer
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### Do differencing within ARIMA or do differencing first before fitting ARIMA

There is a similar question about differencing within ARIMA or before fitting ARIMA. It is stated from the answers that there are differences when differencing is done before fitting ARIMA from ...
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### Differencing vs detrending and test candidates for Time Series

First time I write here but long since I first got into this interesting forum. Well, I'm getting involved with a Time Series forecasting project and I have a lots of questions in my head... but lets ...
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### Math behind Differencing: Is White Noise Stationary?

I'm just starting to learn the math behind stationarity and differencing, so I apologize if this is a silly question. Lets say I have a non-stationary time series process (pure random walk) defined by:...
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### ARIMA first order differencing shows strange pattern

I have came across with a strange issue when I employ a first order differencing to make the original time series stationary. The original ts is with 1-min recording interval and over 2months. Since ...
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146 views

### How to work with multi-step forecasting on differenced time series

I have a financial time series that I wish to make 5 step ahead (t+5) forecasts on. As the series is non-stationary, I have differenced the series. For every time step t, the response variable is ...
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68 views

### modelling on differenced data

I have a time-series data that I want to model using machine learning models like Lasso Regression, Ridge, elastic net, etc. However, in order to make it stationary, I difference the output variable, ...
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### Intuition of second order differencing dependent variable on non-differencing independent regressor regression?

I have two time series sequences. One is $y_t$, which is non-stationary, and the other is $x_t$, which is stationary. Suppose I would like to do a regression of $y_t$ on $x_t$ to forecast $y_t$. The ...
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91 views

### Why would you introduce a constant in a moving average model, when you already have the option of differencing?

In the online forecasting book of Hyndman (https://otexts.com/fpp2/MA.html) firstly the use of differencing is explained. After that he shows the formula for a moving average model: y_t = c + \...