# 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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### Manual Calculation using STL Decomposition

Does anyone know how to manually perform calculations using STL Decomposition? I have this data: Date Count 2017-01-31 68 2017-02-28 59 2017-03-31 75 2017-04-30 71 2017-05-31 70 2017-06-30 68 ...
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### Missing Data in Seasonal Time series. Problems with validation and pre-processing

I have daily data and my goal is to do a 14 day forecast of different product sales in retail. My question is rather about the data and the preprocessing than the models used for forecasting. A ...
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### Declustering impact, stationarity and discretization

I have a seasonal time series, and I am considering declustering (before any other preprocessing steps) it using runs declustering. If I observe an extremal index of 1, can I claim that my data is i.i....
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### how to deal with seasonality in spatio-temporal kriging?

I'm currently working with a spatio temporal dataset of PM10 in North Italy, I have 4 years of weekly data and 160 stations on the region. I seasonally adjusted the time series of each station one by ...
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I have a question on seasonal adjustment. Let's say that I have PPI which is seasonally unadjusted. And, when I look at decomposition plot, I cannot detect seasonality. However, I need to convert this ...
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### Regression Modelling using lme4 in R

I have GPS collar data on a species of desert gazelle throughout different seasons and want to model the effect of seasonal changes in weather patterns on their movement patterns (e.g. daily distance ...
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### Adjusting a multivariate predictive model for drifting seasonalities

This question is a repost of a question originally asked in Quantitative Finance. I was alerted that this would be a more appropriate place for it. I have a time series of daily observations that get ...
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### Investigating seasonality and trend in short time series

I am interested in investigating the presence, or lack of, seasonality or trend in very short time series (typically max 12 observations). Case in point: suppose one is looking at average number of ...
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### Time series : Is SARIMA(p, 0, q)(P, 0, Q) a non-stationary model?

If the data is well explained without any differencing or seasonal differencing but requires some seasonal AR and MA terms, can we say that the data is stationary? I thought SARIMA was designed to ...
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### Predicting a time series containing two periodic components

I am modeling a family of systems whose output is the sum of two time series with different periods. Consider two stationary processes $X_{1i}$ and $X_{2i}$. From this, I generate a time series for ...
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### Seasonal_decomposition with no look ahead bias

I am forecasting the demand for a certain product. The demand dataframe contains a high trend component also some seasonality, for this I don't complicate much and use the method ...
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### Question on decomposition plot (seasonality)

I cannot really understand the presence of seasonality by looking at the decomposition plots. Therefore, I attach two decomposition plots. Is there any seasonality in the series? First one is CPI ...
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### Seasonal adjustment of Brent crude oil price

I need to use the global price of Brent Crude oil (monthly data; Jan-1990, April-2024) The data set is seasonally unadjusted. I decomposed the trend, and seasonality as it's seen in the following plot....
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### How to simulate a time-series based on other time-series that have different seasonality (and other effects)?

I have a list of solar production data time-series for a set of houses in a given area, and I need to simulate the solar production vs time curve of a new house in the area. The sum of the total ...
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### Inconsistent Results with SEATS and X-11 Decomposition Models in R using fpp3

I’m experiencing inconsistent behavior when applying time series decomposition models in R using the fpp3 package and would like some guidance. I have a time series of Broad National Consumer Price ...
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### Converting quarterly growth rate forecasts to yearly growth rate forecasts

I'm generating forecasts on a quarterly basis, focusing on metrics like the GDP growth rate for Brazil. These forecasts are presented as growth rates. For example, the forecast for 2020Q1 represents ...
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### Simulation of Random Processes to Check Stationarity

I am wondering if this is a valid approach: I want to validate that certain random processes are not weakly stationary (constant mean, covariance depends on the lag, finite variance) through ...
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### What is the most common notation to describe cyclostationary stochastic processes?

Can a cyclostationary stochastic process be described as: $\{X_t[i]:i\in\mathbb{N}\}\quad\forall~t\in\{1,2, \dots,T\}$ where variability at the $t^\text{th}$ index across all repetitions/seasons ...
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### Anomaly detection for seasonal data using interquartile range (IQR)

I need to create an alerting bot for anomaly on data regarding funnel monitoring of different product on my company website. The specific metrics I need to monitor are: The conversion rate between ...
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### Cost function for time series anomaly detection with limited labelled anomalies

Given a time series $y_1, \dots, y_n$, I will fit some models to the data and I want to choose one for anomaly identification. I'm interested in a cost function that rewards a model whose fitted ...
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### What is the ARMAX model specification of the following economic setting?

I am currently doing a project estimating electricity prices in France, however, my modelling skills are lacking. I have hourly data on spot prices, which are determined per separate hour, one day ...
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### Seasonality in ECM: Controlling Within the Model (e.g., Adding Dummies) vs. Outside the Model (e.g., Seasonal Adjustment)

When running an Error Correction Model (ECM) with seasonal data, two main strategies are typically considered (for example here and here): Incorporating seasonal dummies within the model to control ...
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### Contradictory Sources on Seasonality being a nonstationarity

I have been trying to figure out whether seasonality means nonstationarity, and the answers from many (often reliable) sources seem to be contradicting. (lets define stationarity as weakly ...
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### Please can I have some guidance on analysing policy change on time series data?

Firstly, I am not a statistician, merely a consumer of statistics (NHS Pharmacist). I am undertaking a project looking at the impact of a new clinical test on antibiotic prescribing across multiple ...
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### How to handle seasonality when using relative errors

I am using a model that forecast predictions for DAUs (daily active users). The DAU dataset is seasonal, so I'm trying to figure out the right "error" function for my model. (The model I'm ...
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### What is seasonality in PROC AUTOREG Durbin Watson Test in SAS?

I want to understand how seasonality for the Durbin Watson Test is defined. If I understand it correctly, the option DW is used for the number of seasons in my data. How can I generally check how many ...
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### Modeling timeseries with strong seasonality

I have monthly national home price index data, from CoreLogic. Data is seasonally adjusted. But still has strong seasonal effect. Here is the plot for monthly changes. ...
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### Should you seasonally adjust time series if hypothesis testing shows there to be no identifiable seasonality?

I have run tests for stable seasonality and moving seasonality. The tests are unable to find presence of seasonality in the time series I am working with. I am wondering if I can still seasonally ...
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### What to do in Box-Jenkins framework when time series has deterministic trend and seasonality?

I'm self-studying time series and I'm puzzled by apparent lack of consistency between : the "classical" decomposition of time-series and the Box-Jenkins methodology. Concerning the ...
1 vote
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### How to remove non-constant seasonality in panel data?

I have a panel data with daily crime rates over seven years. In my regression I control for year, month-of-year, and day-of-week fixed effects (as well as county fixed effects). However, the residuals ...
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### Why does there seem to be a drift in the Arima simulation of a time series with seasonality?

I'm trying to make sense of the basics of time series, and I ran into a block of code by Rob Hyndman. ...
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### Developing a Confidence Interval of Density Functions for Uniform Periods in Seasonal Time Series Data

Suppose I have a set of observational data as a time series where the observations are collected at uniform interval over the course of several years. The data exhibits seasonality over the course of ...
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### How to remove seasonality from time series?

I want to model time series in Python for air quality prediction. My dataset has two columns: date_time and aqi, and contains hourly measurements of AQI. Data is seasonal but not perfectly seasonal ...
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### Prediction interval for linear regression on seasonal data in R

I am using the following code to perform a generalized linear regression which produces a satisfying prediction for this highly seasonal time series. i am just not very satisfied with the prediction ...
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### Decomposition time series

I am studying a daily dataset from a game which contains informations about the peak of players from 2013-2023. This is my first try applying decomposition to see how time series components behaves. ...
1 vote
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### Auto arima capital D

I've got time series 3 years long, there is seasonal uplift during December - but it's not so clear. Seasonal test fails. I train model twice without setting any parameter: ...
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### How to test if a particular frequency is significant or not in a fourier frequency spectrum

I have got a timeseries data with which I plotted a frequency spectrum and I could eyeball all the significant peaks (significant frequencies) in the plot. But I want to do this for a spatial data (...
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### Any numeric measure to indicate seasonality, uncertainty of demand?

Am working on inventory management, demand forecasting etc. As part of this project, I am exploring the data to see the past demand of the products to predict the future. While am currently plotting ...
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### Confused while studying stationarity and autocovariance

I started to study Time Series Analysis and have stumbled on a roadblock. When introducing the autocovariance function, the instructor mentions that we assume stationarity in the data that we are ...
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### ETS (error, trend, seasonal) formulation

Does someone know if there is (clever) way to formulate mathematically all the following models below: in a unique (system) of equations?
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### Controlling for seasonality in marketing mix modeling

I am estimating a marketing mix model on sales using linear regression. My goal is to estimate the effect of marketing and branding on sales (not forecast the future). I have 4 years worth of monthly ...
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### Generate series with multiple seasonality

I have to simulate time series with multiple seasonality and I don't understand how I can do it. In particular I have to simulate: A series with two deterministic seasonality (each with a different ...
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### Random Forest/ Neural Networks for Time Series Data with Large Seasonality

I have been trying to perform Forecasting of a univariate Time Series Data with "daily" recorded observations and exhibiting an "annual" seasonality. The image below depicts the ...
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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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### Statistical Method for Accurately Detecting Seasonality in Monthly Sales Data

I have a dataset containing monthly sales data for different product categories spanning five years (60 months of data). I am using a Python process to calculate the seasonality for each category, ...
1 vote
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### How to obtain seasonally-adjusted time series data using STL in Python

On the section "STL decomposition" in the 2nd edition of Forecasting: Principles and Practice, it says that the seasadj() function can be used to compute ...
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### Monthly data with seasonality: is linear regression appropriate?

I have the following situation: there is data for six years, per month. In a year you can see variation per month, since the data is influenced by the seasons. Also, there is an upward trend over the ...
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### Simulate time series with periodic spikes

I have multiple time series representing a process that operates in batches. It consists of many small intervals interleaved by periodic long intervals (spikes) at the offset of each batch. The period ...
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### Intuition behind testing seasonality hypothesis

In this post to prove the statistical significance of a statement about a seasonality of a timeseries (every april returns are high) the author simulates alternative paths using the Monte Carlo method ...
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