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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why the non-seasonal and seasonal parts are multiplied in ARIMA models?

I would like to understand why the non-seasonal and seasonal parts are multiplied in Seasonal ARIMA models. To be more specific: when we use the Seasonal ARIMA model we assume a multiplicative ...
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Using seasonality in a model

Suppose you are modeling sales of a prepackaged good and suppose there are seasonal periods in the time series. Also suppose that the brand of the prepackaged good you are modeling comprises the ...
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Dealing with seasonality when doing dimensionality reduction

I want to perform dimensionality reduction (in particular, PCA) on a data set that is highly seasonal. One approach that I came across when researching this is "seasonal PCA", where you split your ...
606 views

test of seasonality

I want to test if my series is seasonal, here pacf and the series I'm working on monthly data. is there a test under R seasonality?
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Seasonal adjustment, any major organisation uses STL?

X12 is used by the US government and TRAMO-SEATS by EU governments. Is there any major organisation that uses STL? Since X12 is more widely known than STL, I would like some supporting arguments ...
264 views

How to remove level shifts and pulses from time series?

I am interested in describing seasonal patterns in several time series and then seeing if they are related. My approach is to fit regression models with an indicator variable for each season which ...
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Does a seasonal time series imply a stationary or a non stationary time series

If I have a time series that has got seasonality, does that automatically make the series non stationary? My intuition (probably off) is that it does not. Seasonality means that the series goes up ...
152 views

Seasonal ARIMA Forecast

I'm studying ARIMA at the moment with application to seasonal data sets. R lets you forecast using selected models but I'm just wondering what formula is used to compute these forecasts. For example, ...
10k views

Why should we remove seasonality from a time series?

While working with time series, we sometimes detect and remove seasonality using spectral analysis. I am a real beginner in time series, and I am confused why one would want to remove seasonality from ...
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Choosing the right ARIMA model in MATLAB

I have a problem regarding choosing the right model for historical data that I need to forecast. When drawing the ACF and PACf, a clear seasonality appears at lag 24 as you can see in the figure: I ...
104 views

Correlation parameter with small nonlinear sample like hour / day of week?

I have a dataset of magnitudes Y which gives the scale / magnitude of some event. Each event is also timestamped: Y = [(time1,mag1), (time2,mag2),...] I want to ...
10k views

SARIMA model equation

Can someone please tell me in the book here how is this SARIMA equation obtained? I know that AR(1)=$Y_t=\alpha_1Y_{t-1}+e_t$ Non Seasonal AR(1)=> $Y_t(1-\alpha_1B)=e_t$. My question is what ...
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How to analyze the effects of air pollution separately for the warm season and the cool season

In the model for main effect, we used the R code: ...
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raw data stationary but still can see trend and seaonality is stl

So I am looking at unit sales data. I am doing a univariate time series analysis. My data is weekly sales numbers figures, spanning 2012- 2014 (obviously no till end 2014). I first ploted my response ...
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Stationarity & seasonality in R [duplicate]

I have a weekly number of items sold from 2012 to 2014. 2014 not being complete. So bassically two periods. I am looking at seasonality and stationarity of the response variable (# of items sold) I ...
101 views

Multiple regression for curvilinear seasonal data

This question is related to How to analyze curvilinear seasonal data I have data like following: ...
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How to analyze curvilinear seasonal data

I have monthly values of a continuous variable from many subjects, the mean of which on plotting show curvilinear pattern with lower values in summer months. How can I analyze and report the ...
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Using quadratic programming to fit a piecewise linear model plus seasonality

I am reading this paper on fitting an L1TF model to data using quadratic programming. Section 7.4 states how one could add seasonality to the model however it doesn't go very far into it. I am trying ...
134 views

Compute frequency of time series

I would like to understand how is the period or frequency of time series calculated. Shouldn't a weekly repeating pattern be of the frequency 7, and the yearly pattern be 365? I ask because the paper ...
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TBATS: why set seasonal periods?

While trying to estimate the level, trend, and seasonal components with the TBATS model (forecast pkg in R), I notice that the ...
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Weekly seasonality model by ARIMA+Fourier terms+dummies

This is a long post but it is not conceptually difficult. Please bear with me. I am trying to model the seasonality of production volume of an agricultural commodity. I do not care about the ...
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modeling a proportion with seasonality removed

I have a time series of proportions that typically fall in the 0.01-0.05 range. I had intended to use GLM to model these proportions, but I ran into trouble when I needed to first remove a strong ...
866 views

Fisher's test of periodicity

I have evenly sampled time series on which I applied Fourier transform. I am trying do determine if the signal contains statistically significant periodic components. I have succeeded with determining ...
624 views

STL-decomposition of a time series with deterministic trend and seasonality

what is the relationship between STL-decomposition and deterministic components of time series like trend or seasonality? I have a time series with deterministic trend and deterministic seasonality, ...
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very high frequency time series analysis (seconds) and Forecasting (Python/R)

I have high frequency data (observations separated by seconds), which I'd like to analyse and eventually forecast short-term periods (1/5/10/15/60 min ahead) using ARIMA models. My whole data set is ...
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A dataset I am working with (from the OECD), for harmonised unemployment seems to be seasonally adjusted: The unemployment rates shown here are calculated as the number of unemployed persons as a ...
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How to check if a series has been seasonally adjusted correctly?

I am a bit puzzled here and would like to understand how to check if a time series has been seasonally adjusted correctly using X-13 Arima. After seasonally adjusting time series using X13-ARIMA ...
264 views

Standard model for time series with (possibly multiple) seasonal component

Suppose you have a "new" way to formalize a seasonal component and you want to see if your method is worth to be published. My idea is to take a "standard" model for time series with seasonal ...
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Transforming time series to compensate for change in variance

I have a time series (shown below) that comes from a sensor whose calibration was changed in the middle of last year. As part of this change, the sensor's reading of the variance (or volatility) of ...
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Seasonal vs non-seasonal coefficients in R ARIMA

Let's say I have the two following ARIMA models: ARIMA(7,1,1) (no seasonality) ARIMA(6,1,1)(1,0,0)7 (seasonality of period 7). Are they conceptually the same? If so, why is that when I model them ...
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Filtering using a SARIMA model in R

I am not an expert in statistics, but I would like to work on a SARIMAX model representing power consumption. The exogeneous variable would be the temperature, but for now I found here I might need to ...
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R: Fitting a model with periodic, nonlinear and categorical components

Can anyone give me some advice on how to fit a model with linear (some categorical), non-linear and time series components in R? I don't want to use a non-parametric model like a Loess smooth or ...
611 views

How to check if data needs to be seasonally differenced in MATLAB

I am forecasting data using ARIMA. I would like to know if there is any test to check if seasonal differencing is needed in the ARIMA model. I know R uses Canova Hansen test, but does MATLAB provide ...
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What econometric model to forecast a seasonal commodity demand while incorporating exogenous Information?

I have a monthly commodity demand and try to forecast this series for the next 5 years. Here is a plot: Of course, the natural approach to forecast this seasonality would be some kind exponential ...
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How to perform seasonal adjustment to a time series?

Assume following data set representing each month of the year 2013 with the corresponding consumption of natrual gas to heat my flat and the respective mean temperature. How can I seasonal adjust/...
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I'm concerned to seasonal adjustment procedure and want to know the criteria for this purpose can anyone please give me the answer of the following question. what should be the criteria for seasonal ...
568 views

DLM Trigonometric seasonality vs trend

I am working with a structural time series model in R using dlm that has both a stochastic (slope and intercept) local trend and two trigonometric seasonal components (sin and cos pairs). I have ...
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dlmForecast function in dlm R package forecasting constant values for seasonal series

I have a question regarding the use of the dlm CRAN package for forecasting values of a seasonal time series. I've built a dlm model combining a stochastic local level model with a stochastic ...
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Testing the influence of monthly fluctuations

Let's say we have a dataset that looks like this: ...
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How to calculate the next year's January hourly forward prices for an asset given the historical hourly prices?

I have an exercise given to me during the recruitment process which asks to calculate the next year's January hourly forward prices for an asset given the historical hourly prices of that asset and ...
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Normalizing weekly sales fluctuations in the overall market

I have a rudimentary question regarding how to "normalize" a set of time series data, and would appreciate your thoughts. To make it very simple, the hypothetical situation is as follows: Suppose we ...
529 views

Time Series: Seasonality and trend

I am interested in financial time series and I have a small question regarding the use of the forecast package. The time series I am interested in is a monthly one and present clear evidences of ...
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Is there seasonality or trend in the attached time series graph

Is there trend or seasonality in the attached time series graph ?
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How to calculate time series seasonality index in R?

In R, I use the decompose method on my time series object and it gives me seasonal + trend + random component. For seasonal component, it gives me absolute value which is good but I would also like to ...
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Trying to use Holt-Winters and SARIMA to fit this data

I want to find a time series model for monthly precipitation data. I checked SARIMA and Holt-winters seasonal multiplicative models. I can't find an appropriate model. These models underestimate ...
789 views

How to understand deterministic seasonal component in a SARIMA model?

From Tsay's Financial Time Series, there is a SARIMA model: He said that: I can't understand why deterministic seasonality is special case of the multiplicative seasonal model, and what the ...
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How remove variations in a time series X caused by another time series Y?

I have a time series on a monthly basis (a commodity) of which much variation is caused by the weather. I want to adjust this commodity for weather changes. I use Heating degree day as a proxy for ...
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Strange results in Holt forecast

I am trying to understand what could be causing these strange values to appear on applying a Holt model to a vector. The data represents actual sales of an item. ...