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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Fit and Predicting with Isolation Forest Model

I have time series data that reflects the visitor count from a particular website. So far, I have around a year worth of data and new data comes in everyday. I am trying to predict the anomalies with ...
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Simulating multivariate time series with seasonality

Let's say I have a seasonal multivariate time series xyz with seasonal order 12: ...
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Deal with quarterly or monthly seasonality in forecasting a year ahead

Assume a time series with a clear seasonality with observations every quarter. If you want to use that time series and make predictions four steps ahead, but you are only interested in what the ...
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Difference between seasonality-adjusted data and the trend component

After decomposing the time series, what is the intuitive difference between seasonality-adjusted data and the trend component (from decomposition)?
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Intermittent Demand Forecasting for highly seasonal items

I have a dataset with intermittent sales and very high seasonality and I want to forecast that but it is my understanding that Croston's method only works on non seasonal items. Is there any other ...
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Hypothesis Testing Seasonality in Time Series

Is there any direct hypothesis test in Python that would test for seasonality in a time series without having to decompose the series and interpret the plot?
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Time Series Seasonality and Frequency

I am working with a time series that indicates the number of times a user logs into an application per minute. I want to find an algorithmic way (in Python) that would detect if there is any pattern ...
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Train/Test splitting for seasonal adjustment

At work, I just started dealing with seasonal adjustment of monthly time series on credit data, so being new to the topic it is quite possible that my question is pretty trivial. From what I've read ...
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Deseasonalize multiple independent years doesnt deseasonalize all of them together

I'm trying to grasp time series with a Kaggle project. The exercise I'm currently trying to grasp is this one, which is about deseasonalizing a time series with Fourier series through a periodogram. ...
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Applying regression to a time series where each season has a a linear relationship with a different independent variable

I am trying to apply regression to a problem where I have a time series that I want to predict - say y. Y is seasonal and let's say has 3 seasons summer, winter and other. I have 3 predictors X1, X2 ...
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In multivariate time series regression (say, ARIMAX), should I stationarize and de-seasonalize dependent AND independent variables series?

Second question: when I add seasonal lags (S in SARIMAX) or add month/week dummies to my regression, does that mean I'm accounting for seasonal effects both in dependent AND independent variables?
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Incorporating seasonality in regression #gTrans #rms

I have been looking into incorporating seasonal effects using the gTrans function in the rms R package. However, I am having some difficulty interpreting the statistical explanation in the document. ...
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Non-stationary time-series on visual analysis passes all Stationarity tests?

I have a time-series data (Fig 1) that clearly look non-stationary on visual analysis. There is a clear trend and seasonality in the time series as shown in the Final figure below. But the ADF test ...
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How to forecast a series (daily power consumption) with multiple seasonalities?

I wish to forecast electricity power demand at a mall. Data is collected daily, but, the data has multiple seasonality : data/power consumption is generally similar from monday to thursday but see a ...
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Seasonal variation and long-term trend in Zero-Inflated Poisson / Negative Binomial (ZIP / ZINB)

I am new to time series analysis and I have read a few papers on zero-inflated poisson/negative binomial (ZIP/ZINB) model. I encountered these phrases: "control seasonal variation and long-term ...
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SARIMA initial identification of parameters

I am trying to fit a time series with SARIMA models, where the seasonal period is 7. The figure shows the series after applying a logarithmic transformation and differentiating it for the regular (d=1)...
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monthly seasonality vs annual seasonality with monthly data

I've a time series (monthly data) as in the figure below (it is its decomposition). Then I display in detail a focus of the seasonal plot. Reference to this, I don't understand if the data ha ...
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Test for seasonality with LR-test?

I have an economic time series in monthly frequency. I want to test for seasonality using LR-Test. So the idea is to: Regress the time series y on a model with a time trend and 12 seasonal dummy ...
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How do you estimate the magnitude of seasonality in time-series data?

I have some time-series data showing the monthly counts of hospital admissions. It has both a long-term trend (increasing) and seasonality (highest in summer). I am trying to measure the magnitude of ...
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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 time series data which is generated by accumulating data of every five minutes and reset to 0 by the end of the day. This is the scatter plot of the data. It seems to not matching ...
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Is there some standard way to diagnose a structural time series model (also called simple unobserved components model)?

I am dealing with a structural time series model (also called a simple unobserved components model), and I wonder if there is some standard way to diagnose this sort of models. In most reference books ...
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Getting the right seasonality PDQ for SARIMA model

I am a bit confused about how to identify the seasonal component of a SARIMA model. I am currently looking at forecasting rates (ocean carrier rates to be specific). The first thing I did was to ...
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Find "seasonality" in a categorical time series in python

I have the following sequence: ...
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Seasonal component of STL decomposition looks like the original data

I am doing STL decomposition on Kaggle dataset. Below is just example for one region. I have summed up the values for type (conventional, organic). So data is grouped on date and region. My question ...
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How does the dynamic regression component from TBATS differ from the one in SARIMAX?

Both TBATS and SARIMAX support the modeling of long-term seasonality by using dynamic regression. Dynamic regression in this case involves the use of sin and cos terms to model seasonal components. In ...
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Seasonal and trend adjustment for irregularly spaced time series

I know of different methods that exist to remove seasonality and trend in the data to make it stationary. However, that exists only for regular time series; that is, a series that follows a fixed ...
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Seasonality test for poissonian counts

I have a count $N_i$ of rare evevents for each season, where $i$ identifies the season. The counts' rates are not high enough to justify a normal distribution aproximation of the poissonian. I want to ...
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Is SARIMA(0,0,1)$_\text{s}$ actually MA(s)?

Since for SARIMA(0,0,1)$_\text{s}$ the model equation is $x_t =e_t+a e_{t-s}$, can we say this is a kind of a MA(s) model?
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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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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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Working with a SARIMA Model

Suppose we have the following model: https://i.stack.imgur.com/0jIAQ.png: $$ x_t = \phi x_{t-4} + \omega_t - \theta \omega_{t-1}$$ I'd like to find the parameters of this SARIMA model, as well as the ...
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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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