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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Seasonal and autocorrelated regression residuals: difference raw data or residuals?

I have a multiple linear model for time series data for which the regression residuals are autocorrelated and display seasonal behavior. This seasonal behavior is induced deterministically by a cyclic ...
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Deciding the value of period in seasonal ARIMA (R)

I'm new to time series modeling and am trying to do seasonal ARIMA modeling here. I have figured out the p,d,q values but im not sure how to select the period in the below formula. There seem to be ...
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18 views

Time series object for hourly datat with daily seasonal in R

I have got hourly data from 2012.01.01 to 2016.06.13 and the data shows daily seasonal. I am trying to create a time series object with only daily seasonal in R. ...
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Periodic splines to fit periodic data

In a comment to this question, user @whuber cited the possibility of using a periodic version of splines to fit periodic data. I would like to know more about this method, in particular the equations ...
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Extracting X-13ARIMA forecasts of seasonal effects [on hold]

I am attempting to forecast seasonal effects in various consumer price index components (foods, services, goods, etc.). In other words, I am interested in obtaining - for each time series - forecasts ...
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30 views

Seasonal data deemed stationary by ADF and KPSS tests

I have got two time series and I want to evaluate a VAR model. For this, it is necessary that both time series are stationary. Using R, I have found periodicity ...
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What's wrong to fit periodic data with polynomials?

Suppose we have toy daily temperate data and we want to fit a model. A reasonable thing to do is fitting a periodic model with Fourier basis $$ f(x)=\beta_0+\beta_1 \cos(2\pi x/24)+\beta_2 \sin(2\...
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20 views

Interpreting Seasonality Component Exponential Smoothing Models

I am building an exponential smoothing model that has seasonality in it, I would like to analyze the data with the seasonal factor removed so I can tell if a performance one month was due to seasonal ...
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53 views

Time series prediction in R where data is available over past 4 years in 1 minute intervals

We have data from 'october' in the past 4 years and we want to predict what data for this year is going to look like in October. The data looks like this: 1 2 3 4 5 6 ... Every october has 31 days, ...
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34 views

Using existing time series for seasonal adjustment of new time series

I'm in the process of starting to collect new time series data (monthly observations) which I would like to perform seasonal adjustment on. While I appreciate that there is no mathematically sound way ...
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54 views

Should I adjust a Time Series dataset using X-13ARIMA-SEATS before running forecasts algorithms?

This question is sort of a follow up of this great thread. I have a Time Series Analysis project in which I have to create a model to predict new values given historical univariate data using R. My ...
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61 views

How to deal with hourly non-stationary time series data with multi-seasonality?

I currently have hourly electricity demand data last for 5 years, where I used: demand <- msts(mydata$DEMAND,seasonal.period=c(24,182.5*24,365*24),start=2012) ...
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30 views

trade off between stationary and seassonal time series

I have the annual change in natural logs of house prices as my monthly series. When I undertake the augmented Dickey-Fuller test I observe that is not stationary, and when I plot the auto-correlation ...
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15 views

Selection of additive/multiplicative trend/error/seasonality in ETS

Forecasting: principles and practice. This book tells about 30 different types of ETS models. It describes about additive models and multiplicative model. I would like to know on what basis do we ...
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1answer
63 views

stl() gives seasonal component, but ets() and auto.arima() choose nonseasonal models

I'm completely new to forecasting so please correct me if I'm wrong. I'm trying to forecast sales data using R. My main concern is that when I decompose the data using ...
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28 views

How to manually predict one step ahead time series data using coefficientes estimated by arima function in R

My objective it to manually compute one-step ahead forecast using the estimated coefficientes given by the arima function in R. I will consider the specific model ...
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11 views

Grouping target variable into bins of minimal variance for uniformly-observed, seasonal timeseries data

I am looking at a key performance indicator that is measured uniformly over time for which I strongly suspect seasonality. I would like to create groups to identify periods of time where observations ...
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9 views

Data analysis method for seasonality due to independent variable and trend

I have historical average temperature data for each day for about 30 years. I also have historical data for each hour population of certain kind of microbe. The microbe growth rate is about same as ...
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24 views

Should I be using season as a random or fixed effect?

I am a marine turtle researcher attempting to understand the effect of a harmful algal bloom on our turtle capture rates and the body condition (BC=mass/length^3) of captured turtles. Field ...
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35 views

Making a time series prediction for events per second based on past data

I have data values for events per second (EPS) present in log files pertaining to various devices. The idea is that these values should help us observe a trend and create thresholds for specific times ...
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31 views

Removing seasonality when timeseries includes negative or zero values

I am using an x13-arima-seats based solution to remove seasonality and detect data trends. However, many of the series I need to observe trends on contain zero and negative values, which my solution ...
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33 views

regression model interpretation [closed]

Housing starts = 50 - 7 Mortgage rate + 7 Q1 + 9 Q2 + 7 Q3 Adjusted R²: 0.74 All variables significants is ...
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39 views

How to determine seasonality of a binary variable?

I have a dependent binary variable Y, and an independent date variable X. I want to find out if there is any seasonality (at the year level). A few notes: The binary variable is in my model non-...
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47 views

Time series analysis of electricity load questions

I have hourly data of electricity load (MW) that span 8 months (that is, 5760 data points). I also have predictions from a regression model for the same period. My goal is: to examine some ...
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1answer
34 views

ARIMA with high frequency data of only one month

I'm analyzing some data I collected for 4 weeks I would like to correlate a dependent variable ($y$) to other 10 independent metereological variables ($x_1, \dots, x_{10}$). ARIMA was suggested as ...
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67 views

Decomposing a multi seasonal time series using tbats in R

Can I decompose a time series with multiple seasonalities (an msts object) using tbats (in the ...
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165 views

Seasonality not taken account of in `auto.arima()`

I am having basically the same issue than in this thread, except one thing: The difference, in my case, is that my data is measured weekly and not daily, so the argument of a too high seasonality (> ...
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60 views

Mention day-wise seasonality for forecasting in ARIMA using R

I have half-hourly electricity data of several homes for a duration of one month. This data is represented in xts time-series format. Now, I need to make half-...
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89 views

Choosing the right ARIMA model when data are already seasonally adjusted

I'm trying to build an ARIMA model to forecast the US unemployment rate month-by-month for the period 2006-2015. To select the model I'm using monthly seasonally adjusted data from 1948 to November ...
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1answer
21 views

Which MA(q) to use for hourly data in Time Series decomposition?

I am trying to do a Time Series decomposition manually (I don't wanna use one of those R packages that give you all already done). I have already removed the mean from my TS by dividing the TS by its ...
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35 views

Need help interpreting linear/nonlinear time series

I have a set of data, which i am tasked to find out anything that i could from this set of one dimensional data. Im looking at the ACF and PACF plot. Can anyhow determine if below indicates ...
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1answer
27 views

Using Holt-Winters formula, how do you choose which seasonality to begin your first forecast period with?

This is probably a pretty basic question but I'd like to understand how you choose a seasonality number for the first forecast period in a Holt-Winters model. If you need to forecast 8 months ahead ...
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14 views

Find seasonal variation using multiplicative model

Week 1 237 154 289 349 492 Week 2 249 177 295 362 518 Week 3 258 192 308 376 482 (a) estimate the trend using the method of moving averages (b) ...
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35 views

Identifying outliers in time series with decompose in R

I have time series data, from a period in which it is reasonable to assume the seasonality is the. I used decompose in R to get a multiplicative decomposition. I ...
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50 views

More effective seasonal adjustment to time series data?

I am trying to predict surface temperature using solar energy. I have 3650 daily averages for both variables. The plots of both are below: I attempt to seasonally adjust with a periodic ...
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42 views

Historical data appears seasonal, but forecasts from auto.arima are linear

I am surprised how often the auto.arima function from the "forecast" package in R returns straight linear forecasts when there appears to be fairly strong ...
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28 views

Adjusting for seasonality doesn't seem to work?

I am trying to adjust my data (stored as ts object in R) for seasonality. I have followed the instructions here [missing link]. ...
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21 views

Regression of outcome variable with sinusoidal periodicity?

In linear regression of an outcome variable with sinusoidal periodicity (eg seasonal temperature variation), is it sufficient to adjust for this variation by adding a cosine function [1] as a ...
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31 views

How to model timeseries temperature data?

I would like to model a timeseries consisting of internal temperature data of a greenhouse, collected at 15 min interval and then use it to make predictions in the future. This is how my data looks ...
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35 views

Holt-Winters vs. comparison to history

I have a timeseries with daily and weekly seasonality that I want to check for anomalies (on data as it comes in live). I could use Holt-Winters forecasting, or I could just compare the data with the ...
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79 views

Procedure of clustering seasonality in several time series in R

I want to do cluster analysis of a product monthly sales during 5 years in 30 stores (my data are time series). I want to cluster the stores according to its seasonality. This is an example of my data:...
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26 views

paired t-test with a seasonality

I'm trying to test the hypothesis of whether a certain improvement of the product will affect the consumption of the products. I have a group of test subjects and I measured each test subject's ...
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1answer
21 views

Given a biological dataset with measurements over a year, how can I identify seasonal variation, if any?

I have a biological dataset and I am interested in answering the following question: Are the measurements dependent on time-of-year/season? I use R for my analyses
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30 views

Is detrending the same as seasonal adjustment?

I have a time series of Twitter tweet counts against time. Inevitably, Tweet count goes up during the morning and lunch time. I am exploring the topic of seasonal adjustment. This would remove this ...
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60 views

Time Series Seasonality

how to identify whether seasonality is additive or multiplicative in a time series? Using Plots or any statistical tests?
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13 views

Amplitude and confidence intervals using log transformed dependent variable

I have two questions: - I am fitting a cosinor model to estimate the seasonality of vitamin D levels, which is natural-log transformed. Now, I will estimate the amplitude = sqrt((beta1^2)+(beta2^2)), ...
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24 views

Best method to study seasonality with 53 weekly data of JUST one year? [duplicate]

If you have the data of one year sales of one article, what is the best way to study its seasonality? Note that my data is weekly. So I have 53 weekly data of JUST one year. Is a good way to ...
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127 views

Detecting seasonality with only one full period of data

I have data of the sales of one article in the 53 weeks of 2015 (just 2015) in one shop. I want to study the seasonality of this article. I am having problems with my code in R when I try to use <...
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How to build an adequate SARIMA model?

I'd appreciate some help with my data. I have to find (S)ARIMA models to fit some exportations data, but for some of them, I can't find an easy model by just looking ACF and PACF plots. So I change ...