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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Time series data with seasonality using model VAR and VARMA [duplicate]

I have a time series with seasonal economic data, and other time series to see if this variable help predict my time series, but the VAR model is not a model for seasonality. What options do I have ...
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What's the best preprocessing steps to take in seasonal time-series models?

Consider for instance this model simulation done on 100 data points what are some considerable preprocessing techniques that one might use for this type of model? I notice there's a trend in the time-...
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identificar y estimar, validad, predecir y comparar con Alisado. ARIMA

I would like to know if there is a function that can filter work days in my temporary serie. I need to include 2 intervention variables, easter days and work days, in order to estimate with Arima I ...
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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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How to test if day of week impacts a stock's return

Say you have the daily % change in a stock's price going back a few years, looking something like this: ...
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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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Test for distribution equality

This question touches Kolmogorov-Smirnov testing, but asks actually something different. Consider independent random variables $X_1, \dots, X_n$. I want to test the following hypothesis: $$ H_0: X_i\ ...
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Adding "weekly" seasonality in arima R

I've found the internet fairly unhelpful with this issue and thought I'd turn. I have the following arima model: ...
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How to model seasonal variance in a high frequency time series?

I have a time series that exhibits a clear seasonal pattern regarding its variance. Basically at night and morning the variance is low and at midday it is high. The time granularity of the data is 5 ...
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SARIMA mathematical expression

In this video: https://www.youtube.com/watch?v=IK67f3IItfw at 4 min mark, Dr. Aric LaBarr shows an example of the following model: $ARIMA(1,0,1)(2,1,0)_{12}$ his resulting equation is: $W_{t}=c+\phi_{...
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Does seasonality frequency matter in exponential smoothing?

I'm pretty new to time-series forecasting and I hope that someone could help me out. Referring to Holt-Winters' multiplicative method in https://otexts.com/fpp2/holt-winters.html, how does frequency ...
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Select the best period value to visualize clearly the Trend and Seasonality

I have a daily data for 4 years range between 2016 - 2019. I used statsmodels.tsa.seasonal.seasonal_decompose to decompose the seasonality and trend but I should ...
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Linear Regression on data with seasonality

I have a dataset of temperatures for a few decades. Data looks a lot like on image, with seasonality. The question is whether it is possible to draw conclusions about how the temperature is changing ...
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Mitigating seasonality and conditional heteroskedasticity

I came across this question online that's from a math/stat challenge a while back. Would love to get some thoughts on what the correct answer should be: You're trying to assess transit usage trends in ...
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Seasonality in Independent Variables

There are many questions on why we need to remove seasonality. E.g. this and this. My question is slightly different. Do, we need to remove seasonality from independent variables as well when doing ...
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Can you shift a time series and multiplicatively decompose it afterwards to not have negative/zero values

THis question refers to the last unanswered comment in this question: Decomposing a time series with some zero values I see, thank you for the explanation. Let's suppose that the time series follows ...
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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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Seasonal differencing a when the sample size is small when estimating a VAR

When estimating a VAR the series must be level and seasonally stationary. However I have only 48 data points. I first made the series level stationary based on the ADF test and performed HEGY test for ...
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SARIMA(1,1,1)(0,1,1)7 Math Formula

Would the correct mathematical way to write a SARIMA(1,1,1)(0,1,1)7 Model be: $$ (1-\Phi_1B)(1-B)(1-B^7)y_t= (1+\Theta_1B)(1+\Theta_1B^7)\varepsilon_t $$ I am new to the ARIMA world and I am trying to ...
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Why does the level update equation change in triple exponential smoothing (but the trend equation does not)?

I'm confused on the level and seasonal update equations in Holt-Winters (aka Triple) Exponential Smoothing. Namely, the equations are as follows (in additive form): Level: $l_t =\alpha(y_t - s_{t-m}) +...
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Statsmodels seasonal decompose interpretation

I'm currently working with a time series that has a monthly frequency. It has 3 years of data, 2019-2021. When using the statsmodels.seasonal_decompose I got the following plots: I would like to know ...
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Modelling seasonality by means of Fourier decomposition

I'm trying to model seasonality of a time-series by means of Fourier decomposition in order to model some yearly recurring patterns. The Fourier decomposition consists out of a few steps. The time-...
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What to do with missing days from timeseries when checking for seasonality?

I have a dataset which looks like this, with pm25 values and timestamp as index: ...
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Why I cannot find suitable ARIMA model for the dataset?

I have a monthly dataset. I applied ADF test and saw that this dataset is stationary. Also, Canova-Hansen test is applied to see if there is stochastic or deterministic seasonality. As you see below ...
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How to predict monthly data from quarterly seasonal data?

I have a dataset that contains the price of a vegetable for each quarter-end day since 2000-01-01. Now I want to get(predict) the monthly values of the month-end prices. I am not a student of stat, by ...
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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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Forecasting cross-evaluation under seasonality: fix day of month of the training/test splits?

I am currently working on a time series forecast model that, on the 15th of every month, will predict daily values for the next month (e.g., on January 15th, it will predict values for every day of ...
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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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AutoARIMA performance

I am trying to implement a pmdarima AutoARIMA estimation exercise for learning reasons. Observation is that, selected model fits the train data quite well, however it performs poorly on test data, at ...
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Harmonic regression to estimate seasonality component in R [duplicate]

I would like to estimate the seasonal component in the series a below using harmonic regression. I am new to harmonic regression so would appreciate someone showing me how it works and how it is done ...
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Breakdown and interpret the ARIMA model

Electricity usage goes up during winter because heating is used Electricity usage goes up during summer because air conditioner used. $$y^*_t = \beta_1x^*_{1,t} + \beta_2x^*_{2,t} + \eta_t,$$ $$(1-\...
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Interpreting ACF and PACF for data which have had its seasonality removed

I'm currently working on a project and trying to figure out how to interpret my ACF and PACF plots. I have removed seasonality from the data in order to establish the trend, now when plotting my ACF ...
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Seasonality and panel data

I am working with panel data observations. One of the principal characteristics is the strong seasonality. I know that i could control it using dummies variables. My question is What would happen if I ...
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SARIMAX statsmodels model_fit.forecast predicts NaN values after 52

I have a dataset of bike renting between 2014 and 2020, and I want to use data between 2014 and 2018 to predict future usage, and to test it on 2019. However when using predict, I get Nan values after ...
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Intuition underyling kinds of time series that are typically additive or typically multiplicative with examples

What is the intuition underyling the kinds of time series that are typically additive or typically multiplicative? From what I understand, additive time series are such that variations on the trend ...
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Can TBATS be used in the case of deterministic seasonality?

I have a monthly dataset which consist of 176 points. I validated that it is stationary by adf.test and it has deterministic seasonality by ...
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Error in auto.arima with seasonal dummy variables [closed]

I have a monthly data set for 15 years. I tried to apply SARIMA model on it. However, thanks to the comments here, I realized that it has deterministic seasonality. So I add seasonal dummy variables (...
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Identification Problem of SARIMA

I am trying to make time series analysis with SARIMA and I have a question. My dataset is a seasonal dataset. I validated that I have stationary series by KPSS test. I also found the following ...
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SARIMA Equation interpretation

I'm building a SARIMA model in Excel, but I'm not sure if I follow the deffinition with Lag operators $L^n$. For a $SARIMA(p, d, q)(P, D, Q)_m$ model, are the following equations right? $$\Delta_{m}^{...
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The contradiction in KPSS and HEGY test

I am new to this field and I have a question. I have a seasonal rainfall dataset and I want to apply SARIMA model on it. For this purpose, I applied the KPSS tests and I got the following output: <...
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Does this ARIMA model take seasonality into account?

I'm writing a tutorial on traditional time series forecasting models. One key issue with ARIMA models is that they cannot model seasonal data. So, I wanted to get some seasonal data and show that the ...
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How to interpret the HEGY test?

I performed the HEGY test on the level stationary data to test for any seasonal unit roots. Given below is my output. Should I conclude that there exists unit roots based on the output since F11_12 is ...
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Splitting my forecast data in an optimal way

I have monthy historical data from 2017 to 2021 as seen below: * 2017 - 1 - 1 4000$ * 2017 - 2 - 1 7000$ ... * 2021 - 11 - 1 5000$ * 2021 - 12 - 1 1000$ ...
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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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Can you suggest a novice method for detrending and deseasoning time series to find relationship between two variables?

I have a time series with two variables: discount and sales. My goal is to figure out how the discount affects the sales. I want to perform regression. However, the sales data has a trend and ...
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Does this seem like a seasonal effect? [duplicate]

I have tried to produce a seasonal fit onto a time series, and I got this result where all the amplitudes are consistent. Would you say this plot is valid or do I need to adjust it?
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adfuller test say its stationary but decomposition shows signs of seasonality

I am working with this time series and i got confused; adfuller test says it is stationary as p-value(1.1125518783299598e-29) is less than 0.05, acf and pacf shows no significance(see image), ...
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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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