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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Model selection for and forecasting of arctic oscillation (a seasonal time series)

I'm having a doubt with a time series. I have to find the best model for it and use it to do some forecast. The data are about the arctic oscillation (AO) from 1950 to 2015. The series is clearly ...
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21 views

X-13 Seasonal Adjustment trading day peak in regarima residual

I have a time series of air passengers with a total of 143 monthly observations. Having done the seasonal adjustment using X-13-ARIMA-SEATS, the final diagnostics seem to suggest that the seasonal ...
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9 views

References for Combine Seasonal Period in Seasonal Time Series

I'm in a middle writing my thesis. I got confused for find the references which said period of seasonal could be chosen from the small period which already containing another periods. Here is my ...
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24 views

Modelling effect of advertisement on sales with ARMAX

I am trying to model the effect of advertisement on sales in Stata. The data is weekly and there are around 150 observations. I started by applying an ARMAX(1,0,1) model with the following exogenous ...
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11 views

Residual Not Normal for Model Seasonal Time Series in R

I got a problem when choose the model for forecasting with time series. I'm in a middle writing my Thesis. My data have a seasonal pattern so, i tried use this model ...
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20 views

Fitting a model with time of day, day of week adjustment

I have one year's worth of clickstream data (like Minute, Numvisitors). I'm trying to see whether external events (commercials) affect ...
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25 views

finding seasonality in data

I have a dataset that looks to have some periodicity to it (given the nature of this data, the pattern was not expected): Visual inspection of a small part of the graph tell me that the frequency ...
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56 views

Why do we deseasonalize data?

I am reading an article in which the author claims the means and standard deviations for the annual weather data she's studying vary along the years; i.e., every year has different mean and standard ...
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60 views

Cross-correlation between two seasonal series

To determine cross-correlation between Sales and Variable cost, both having monthly seasonality, do I need to de-seasonalize ...
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80 views

How to assess seasonality effect influence on time series

Suppose I collected a time-series data (e.g. drug prescription on every month for 12 years). I have no reason to believe that my data is influenced by a seasonal factor (e.g. drug consumption is not ...
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21 views

Multiple Seasons msts R fpp

I am trying to use the fpp package to do some forecasting in R My figures are daily and the seasonal trends include week, month and year. Week and year seem easy: y <- msts(x, ...
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2answers
92 views

Periodicity and seasonality of a time series

I have a time series and I have done some spectral analysis on it. When doing an autocorrelation and periodogram it shows that the time series is periodic. However when I do a Dickey-Fuller test it ...
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24 views

How can I test for seasonality when the trend is not supposed to be monotonic but sinusoidal?

My knowledge of time-series analysis is limited. So far I have only assessed whether there was a seasonality in my time series data with the assumption of monotonic trend. To test that I would have ...
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41 views

How to forecast weekly sales data using R and `auto.arima`?

I have weekly sales data with for thousands of products which I want to forecast in an automated manner. What I clearly observe in my data is that there is a weekly skew within a month (wk1 sales < ...
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11 views

Correlation but with magnitude included - best fit line?

I want to analyze which industry forecast best predicts my business. I have 2 to choose from. I have found that they are all highly correlated, but I suspect one may be also closely related by the ...
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17 views

How to write this ARIMA model mathematically? [duplicate]

I am trying to analyze a time series: I see a strong seasonal pattern, so from every value, I subtract the value from the same month the previous year (12 periods prior). Also, I am using 1 AR term ...
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66 views

SARIMA models: Good fit and stationarity

I'm doing a study where I try to fit two different data series to two different SARIMA models. Both series includes trends and seasonality (daily and quartely, I think) and I'm having problems to make ...
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49 views

Time series of variance

If the mean or total of a variable studied over time displays seasonality, should I expect that the variance of that variable should display seasonality similar to the mean? Why or why not? The data ...
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20 views

Variance on Extreme Seasonal Time Series

I'm trying to come up with a decent method for forecasting a unique seasonal time series that is involving multiple periods of seasonality: Weekly, Monthly, Quarterly and I am stuck because I have ...
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33 views

How do I model seasonal patterns for underprediction?

I want to predict sales in food-vending machines (to ultimately prevent food waste). I work with scikit learn. My current models are not too bad, but they show ...
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21 views

Test if Google searches differ by week of year

I'm looking into resuscitation related search queries using Google Trends. I see that the rate of resuscitation relevant searching falls dramatically each December. I'm not sure how to test for the ...
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1answer
53 views

ARMAX model and validation

I am new to time series and am trying to fit some time series data. I understand the general concept of ARIMA model. However, as I read more textbooks and articles from Rob Hyndman, I realized I ...
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1answer
64 views

SARIMA with dummy variables for double seasonality

I have a series with double seasonality, one daily and one weekly. I modelled the daily seasonality with SARIMA, and I want to include weekly dummy variables. I only included weekday variables for ...
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21 views

Given sales data for a product, what is the best way to calculate the trend period for it?

I am looking for a statistical way to calculate an approximate in-trend period for a product from its sales data over a time period. Of course, in the 'in-trend' period, the sales of the product ...
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76 views

Adjusting daily time series data for the seasonal component

I have a time series data containing roughly 13 000 daily observations, and the initial plan is to fit them to an ARMA model. I have adjusted the data for deterministic trend with a regression model, ...
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20 views

Irregular Seasonality in time series

I understand seasonality of a time series normally means a cyclic component with constant frequency. For example, the frequency is 24 for daily cyclic trend of hourly data. One of the basic models ...
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1answer
15 views

How could I seasonally adjust data series and constrain produced data only to 0 or positive values?

I would like to seasonally adjust data series that cannot be negative. How I could do this? Currently I am using seas in R. Is it possible to constrain the output series to 0 or positive values?
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Computing Seasonality Index and application to shorter time series

Background: I have an overall time series of close to 3 years of data. I need to forecast for different slices of data. When I slice the data, some slices results in a shorter time series. We go with ...
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30 views

Different seasonality patterns

I'm currently trying out several ARIMA models for time series data with seasonality. The data consists of daily demand for two years. The data has strong weekly seasonality since Fridays and ...
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22 views

I have two time series recorded on a weekly basis that have a quadratic trend. Should I difference the series twice with lag 1?

I have two time series on google Trends weekly data for the search of the terms 'machine learning' and 'data science'. The data can be found here ...
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1answer
57 views

fourier terms for double seasonality in R [closed]

I am performing a time series analysis on a daily time series. I know that there is a weekly period (7 days) and also a montly seasonality. For now, i set the time series object in R using a ...
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1answer
55 views

Why after including lags do seasonal dummies become significant?

I am trying to model data that clearly looks like it has seasons. However I only pick up seasonality in very small subsets of the data and only after I add in lagged variables and eliminate trend. I ...
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1answer
61 views

What are the implications and possible explanations for an AR(7) process model?

I am in the process of constructing a regression for financial data and found that serial autocorrelation is present in the model through the correlogram: It looks like it could be an AR(7) ...
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112 views

tbats with weekly, monthly and yearly seasonality not working

I am trying to predict values based on a dataset which may contain weekly, monthly and yearly seasonal data. To simplify things I am assuming that all months have four weeks (28 days) and the year has ...
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79 views

Seasonal adjustment a la Hyndman

Rob J Hyndman has two posts here and here on forecasting weekly series. He suggests using a regression with ARIMA errors, $$ y_t = a + \sum_{k=1}^K (\alpha_k \ \text{sin}(2\pi k t/m)+\beta_k \ ...
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34 views

count time series with multiple seasonality

I am analyzing a time serie (hospital admittance) registered by date - time at hourly frequency, collected all days during 2010 - 2014 (5 years). The time serie exihibits seasonality at multiple level ...
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112 views

Daily data regression - setting up dummies

In order do make a regression for daily sales data i need to set up different dummies (e.g. day of the week, monthly, yearly, week of the year, moving holidays...) ...
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1answer
26 views

Why use detrending methods when studying seasonality of a phenomenon?

I have a basic question, I am trying to study the seasonality of birth in a town, and all the material I am researching use moving average for detrending and these values are eventually used for ...
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Double-Seasonal Holt-Winters forecasts for periods where $k>s_1$

I have the feeling that this may be a stupid question, so apologies in advance. I have a set of daily demand data (midnight-midnight) which clearly has two very strong seasonal cycles - one ...
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1answer
88 views

X12 for seasonality adjustment - SAS

I found this code online and I wanted to dissect it before programming something similar in SAS. The problem is idenitfy seasonality in a time series. I want to understand the code line by line: ...
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20 views

Which technique will tell whether mortality is seasonal or not?

I want to analyze monthly death counts with respect to age, cause and gender. The data I have is about the name, date of birth, date of death, gender and cause of death of about 2000 cases for the ...
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30 views

A smoothed series still exibits strong seasonality

I have a monthly time series. It is basically a price level series (inflation data), and I converted it into monthly percentage changes (i.e. like the CPI measure). This time series exhibits extremely ...
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56 views

How do I assess seasonality with a glm using a cosine curve in r?

I'm new to R, so I'm sure I'm just doing something dumb. I have a dataset of kereru counts from two different decades, the 80s and 2000s. I am looking to describe how kereru counts have changed ...
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1answer
112 views

How to identify the seasonality of a timeseries from the Periodogram?

I need to identify seasonality/ periodicity of a dataset so as to develop an ARMAX model. This is what the original time-series looks like I have plotted the periodogram of the dataset. Ps: I used ...
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80 views

How to include seasonality in the data ARMAX model that has multiple periodicities?

I am doing regression with ARIMA errors. The residuals are as shown in the figure below. Clearly, the scatter plot shows that this time series has some sort of periodicity or seasonality, but its very ...
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34 views

How can I filter marketing campaigns out of my decomposed seasonal data?

I've recently jumped into the deep end of statistical analysis of revenue. I've learned a ton about statistics, probability, decomposition (stl), and the Python and R languages. I feel like I'm ...
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1answer
24 views

Cross-applying known seasonality adjustment to new data

I have two sets of data, drawn from the same source. I know that the data exhibits seasonal behavior, visible over each week and over each day, and am willing to assume that the seasonal behavior is ...
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1answer
324 views

Decomposition of daily time series (several years) with multiple seasonal patterns

i have a daily time series of several years. Graph & CSV-file So far i could figure out with an based on an acf graph and this method: timeSeriesObj = ts(x,start=c(1999,1,1),frequency=7) ...