Questions tagged [seasonality]

Seasonality refers to the recurring fluctuation around the mean of a time-series for a given period of time, usually a calendar year.

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How do I identify if my time series' seasonality is additive or multiplicative?

The "ExponentialSmoothing" function in Python's "statsmodels.tsa.holtwinters" library gives you the option to set trend equal to ...
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What is the correct way to evaluate time series forecasts with seasonality?

I am working on an energy demand forecasting project, where I am using the Facebook Prophet model. I have used 3 years (2017-2020) of training data to forecast energy demand for a week at an hourly ...
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Regression with SARIMA errors

After an SARIMA transformation, is $\epsilon_t$ equal to the difference in observed original $y_t$ from its estimate or the equivalent quantity for transformed $y_t$, $y'_t$? The motivation: I am ...
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SARIMA explicit formula

I'm trying to expand the $\mathrm{ARIMA}(1,1,2)(1,0,1)[7]$ model to get the explicit formula. Writing the model with polynomial operators should be $$ \phi_1(B)\Phi_1(B^7)(1-B) x_t = \theta_2(B) \...
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Do you need to seasonally adjust covariates prior to ARIMAX modelling?

I found lots of answers in regards to how handle seasonality in dependent variable (time series) though can’t find a definitive answer if we need to seasonally adjust the covariates as well? My main ...
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Residual is identical to Observed in Seasonal Decomposition

I am trying to understand my dataset using the seasonal decompose function from statsmodels. The trend and residuals of my dataset are awkward. I am used to trend being either an upward or a downward ...
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Why strong seasonality in time series of total shipped volumes not observed in customer groups?

In a time series dataset, demand from various customers are given on a daily basis. When the data is aggregated at month level for all the customers together it is easy to see the effect of quarterly ...
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Should I plan my AB testing accordingly to a minimum number of days or to the number of datapoints?

Here's the thing, I was planning to test a new strategy on my website. A typical AB test for a new homepage. One strategy is the current, the control; the other is the variant, the new strategy. I ...
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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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How to identify a non-periodic time-series?

I am working on a problem where I have to first classify whether a time-series is periodic or not and then, if it is periodic identify its period(s) (the time-series could have multiple periodicities, ...
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What does residual value of 1 mean?

I am using statsmodels seasonal_decompose to visualise components of time series and I'm trying to figure out how it works. I have these time series: When I try to use additive seasonality parameter, ...
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What's a proper method for analyzing an intervention in a seasonal time-series?

My data has the following structure (I cannot post the real data): The data contains 20 shapes (round, squared, triangle), 2 were chosen for simplicity. The data is recorded for almost 2 years (aprox ...
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Identifying extreme values in seasonal time series data

What are some commonly used statistical tests for identifying extreme values in seasonal time-series datasets? Should it be something on the lines of a) fit a distribution to the data, b) identify ...
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Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline)

I am trying to fit a hurdle model to seasonal data for which the day of the year is known. To this end, I tried to construct a spline with cyclic restrictions (ends meet beginnings). Here is a MWE ...
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VAR (Vector Auto Regression) with exogenous variables

Is it possible to set seasonality as dummy variables in a VAR model? Which I use those dummies as my exogenous variable?. Is it also advisable to input other variables that are a good measure of my ...
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Does trend and seasonality need to be removed before making forecasts with ARIMA model?

Is it necessary to remove trend and seasonality from time series before making forecasts with ARIMA or can the model handle them by itself?
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Interpreting seasonal detrending

I am learning about detrending data using seasonal decompose with the Gold Futures contracts: ...
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Interquartile range to detect anomaly for quarterly data

To detect anomaly for monthly data, I calculate interquartile range using the previous 12 months of data and check the current month data against that range - if the data is presented quarterly, can I ...
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How to remove inter-year variation from my assessment of seasonal varriation

I have a 30 year dataset of fish sampling. I know from previous analyses that there is a huge amount of variation between years in catch rates. What I would like to do is create a descriptive plot ...
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How using a Fourier Series to model seasonal data with ARIMA works?

My understanding is that if we have a seasonal time series with period of $m$ we could model seasonal data by approximating the time series as $y_{t} = a + \sum\limits_{k=1}^{K}[\alpha_{k}]\sin(2 \pi ...
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How to interpret statsmodels seasonal_decompose

I have apple stock prices time series over 1 year and I have tried to use statsmodels seasonal_decompose to obtain information about it. I am very much a beginner with time series and I'm not too sure ...
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35 views

Difficulties and possible adjustment measures of forecasting stock prices

I understand that a non-stationary time series have fluctuating mean and variance (and ACF) over time. In my case for stock prices, it is leaning towards having cyclic pattern rather than seasonal ...
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Decomposition plot interpretation

I have a question about the interpretation of a decomposition plot. From Hyndman's book "Forecasting: Principles and Practice" which results from a classical additive decomposition model of ...
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ICC for seasonality

Is there a way to calculate icc for seasonal variation? icc would describe how much variation in seasonality that can be explained by different groups' group-specific characteristics.
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Auto.arima application in R with sub-daily data - No seasonality given [duplicate]

I'm working on a R code and my aim is to make forecasts with a model chosen by applying auto.arima function on my data. These are recorded every 6 minutes, so we're dealing with sub-daily data. ...
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Seasonality and ECM/VECM - Correct seasonality before estimating VECM

I know that for univariate framework, a typical process to deal with seasonality is : detect correct (for instance, withdraw seasonal factors) forecast re-seasonalize the forecasted series (for ...
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Including a “year” effect in an LSTM sequence-to-sequence model for time-series forecasting

I am working on a problem to forecast some climate sensor data. I have data that includes daily sensor measurements from 1980 till present. Now I have written a Sequence-to-Sequence LSTM model that ...
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Frequency of timeseries greater than half the number of datapoints in timeseries

as suggested in the following thread: Period detection of a generic time series I'm testing the function findfrequency() to automatize the estimation of the period ...
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Can Seasonal ARIMA model be expressed without backshifts?

Every equation of SARIMA I have found involves backshifts. I was wondering if I have an ARIMA model expressed like this: is it possible to express it in a similar way, without backshifts? Are there ...
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What are the possible problems with using ACF to detect frequency in timeseries?

Looking for a way to detect frequency without knowing anything about the timeseries beforehand. I ended up as suggested by another user in this thread: Period detection of a generic time series Here ...
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Influence of Seasonality on Unit root tests

I gather from this question and answer, a seasonal series is non-stationary as its mean depends on which month it is. Suppose I have a series which possibly has a unit root (stochastic trend) but also ...
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Trend Dampen with SARIMA

Trend dampen exists as a parameter for Holt-Winters in the ExponentialSmoothing class for statsmodels but how can I do something ...
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Seasonal spikes in residual ACF plot for a Fourier regression ARIMA error model

I have recently fit a Fourier regression ARIMA error model to some time series data, which has weekly and yearly seasonality. The model is of this form (except there is another sum since I have ...
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Joint Test for Seasonal Forecasting Model using Dummy Variables

I recently created a seasonal dummy regression model in R given a dataset beginning Jan 2016 and ending May 2020. Given the results below there appears to be statistically significant seasonality in ...
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statsmodels seasonal_decompose forward looking bias?

I'm using the python module statsmodels to do an additive seasonal decomposition of a time series. I have been trying to understand if the method used looks at the whole series at once or if it only ...
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Seasonality estimation without knowing the number of observations per seasonal cycle [duplicate]

I'm trying to detect if there's any pattern (seasonality) between login attempts on a machine using python. After researching a little bit i stumbled upon the library pmdarima, providing statistical ...
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Check for a disease seasonality

I want to see if there seasonality to a disease Im looking at an autoimmune disease that has several subtypes, characterized by different autoantibodies (lets call them autoab1, autoab2, autoab3). I ...
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1answer
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Use of ACF and PACF

I am new to time series analysis, I have come across ACF and PACF while working on time series data set. There is a confusion, in some links/texts ACF and PACF is plotted without taking difference i.e....
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Second of the seasonal difference in a time series

Please let me know how to do the second of the seasonal difference in a time series. For example, I have 7-day seasonality and I did the first and second differencing as follows. I got the following ...
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Model specification for seasonal ARMA-GARCH model using rugarch

TL;DR: I'm trying to find an adequate model for time series data that exhibits multiplicative seasonality and volatility clustering by identifying an ARMA-GARCH-model with Fourier terms using ...
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How to detect deterministic vs. stochastic seasonality graphically

There are some threads about deterministic and stochastic trends here. But I have not found a thread regarding to this question: Let's assume I have a given time series plot with a seasonality (and ...
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Automatic detection of seasonality on a time-series [duplicate]

I have been workin with time-series data. I haven't been able to find any way of analysing automatically if a given time-series has a seasonal behaviour (when I say automatically, I mean in a way I ...
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Combining SARIMA and STL models

Can we integrate SARIMA and STL for anomaly detection? If so, what is the process like? Which model do we run first and what input goes into the other model? I am fairly new to time series so pardon ...
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Accounting for multiplicative seasonality by including external regressors in ARIMA-GARCH model using R?

At the moment, I'm trying to model a time series in preparation for a multivariate analysis. The time series comprises tweets per hour for a period of nine weeks. As you can see, and as is to be ...
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Testing means in presence of autocorrelation

I am working on a project and I am currently studying a dataset of energy consumption. In order to perform a more precise modelling, I thought it was reasonable to split daily consumption in 2 ...
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Time series analysis: multiplicative model and seasonal adjustment of data

I am trying to help a friend in statistics and this question involving time series came up and I did not know what to do. I tried searching different stack exchange forums for answers, but I believe ...
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Upsampling multi-seasonal data points to fit known averages and avoid discontinuity

Context: I am trying to forecast nationwide demand for a water system. The system I am modelling is highly seasonal (with daily, weekly, and annual seasonalities, at least). The challenge: I already ...
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How to calculate the expected value of a time series just from the data

in this question Can stationary time series contain regulary cycles and periods with different fluctuations I was told that stationary time series do not have regular cycles and that having constant ...
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Seasonal regression with temperature data

I have a daily collected time-series of temperature data that goes from 1981 to 2018 that look like this: ...
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Using variables in VAR model after 1st order differencing

I am trying to build VAR model with two variables - Median Sale Price and Average Mortgage Rate (both monthly). 1) Plotting initial data and this Applying the 1st order differencing, because the ...

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