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 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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ADF tests: phi2 and phi3 explodes when differencing
ADF tests are used to inform on the order of integration of a time series. With the function ur.df, three different specifications can be used, called "trend&...
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Are non-constant polynomial means a special case of seasonality?
In this video, it is said that an otherwise-stationary time series with non-constant linear mean is analyzed by taking the first difference of the time series to produce a new, stationary time series. ...
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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{equation} \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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Prediction intervals - "VAR in levels" vs "VAR in differences"
The prediction intervals are much wider on my "VAR in differences" model than in my "VAR in levels" model. Any ideas of why this might be the case? I know there is a strong ...
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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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Time-series process with a difference close to zero
Suppose that we have a balanced panel data set, $\{Y_{it},X_{it}\}_{i=1}^N$, where $Y_{it}$ is a binary outcome variable and $X_{it}$ is a vector of covariates.
Then, consider a linear specification ...
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ACF and PACF graph interpretation problems
i am plotting here the graphs of the autocorrelation plot of my data done with python prior and after making the differentiation
I do not understand the two trends of the paths after differencing ...
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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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Detrending multiple predictors
I feel this is probably a stupid question;
I have 3 time series (x, y, z). Time series x and y have a more or less time^2 pattern (i.e., curvilinear effect of time), whereas time series z is basically ...
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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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Differencing white noise
(1) Is a first difference of iid white noise also iid white noise? For instance, if
$$y_t=e_t$$
with $e_t \sim \text{iid w.n.}$, then is $y_t-y_{t-1}=e_t-e_{t-1}=w_t$ with $w_t \sim \text{iid w.n.}$?
(...
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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. ...
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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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Sum of $I(1)$ and WN
Is the process $\Delta Y$ an MA(1)? $Y_{t} = X_{t} + w_{t}$ with $X_{t} = X_{t-1} + e_{t}$ and $e_t$, $w_t$ both independent white noise a MA(1) process?
What I did is the following:
$(1-L)X_{t} = e_{...
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Is non-stationarity an issue in this setting?
I am trying to model the development of European spot prices of gas. My purpose is to explain what has caused past movements in the gas price, rather than forecasting future gas prices.
Naturally, ...
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Reverting differencing for Time Series VAR model component wise?
I have data with seasonality so I used seasonal and then first order differencing to make the series stationary in order to fit VAR model.
After the model is fitted on the differenced level I can ...
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For time series forecasting using machine learning, is feature engineering only needed for the y variable or is it needed for all x variables also?
Say I am trying to predict house prices (y variable) using population growth and GDP (x variables) using XGBoost or Neural Networks. All 3 are time series. I understand that I have to feature engineer ...
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For time series, is non stationary an issue for machine learning models like they are for traditional time series models like ARIMA?
Sorry if the question seems basic. I understand that non stationary data is a big issue for traditional time series forecasting methods like ARIMA and VAR but is it the same for machine learning ...
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Percentage change and then Rolling average V.S. rolling average and then percentage change
For a timeseries data $\{D_t\}$ with some seasonality $s$ and high volatility $\sigma$, we often want to perform a rolling average $\frac{1}{n}\sum_i D_{t-i}$ to denoise the data and take some ...
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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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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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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 ...
