29 votes

Trend in irregular time series data

Rather than try to decompose the time series explicitly, I would instead suggest that you model the data spatio-temporally because, as you'll see below, the long-term trend likely varies spatially, ...
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27 votes
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Daily Time Series Analysis

Your ACF and PACF indicate that you at least have weekly seasonality, which is shown by the peaks at lags 7, 14, 21 and so forth. You may also have yearly seasonality, although it's not obvious from ...
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21 votes

MLE convergence errors with statespace SARIMAX

First, mle_retvals should be an attribute of SARIMAXResults if it is constructed using a fit ...
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  • 1,243
17 votes
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Why Time series decomposition is performed

Time series decomposition helps us disentangle the time series into components that may be easier to understand and, yes, to forecast. In principle, yes, you can see pretty much everything in the ...
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13 votes

Does a seasonal time series imply a stationary or a non stationary time series

IMHO, persistent seasonality, by definition, is a type of non-stationarity: the mean of a seasonal process varies with the season, E[z(t*s+j)] = f(j), where s is the number of seasons, j is a ...
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13 votes
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Is this an appropriate method to test for seasonal effects in suicide count data?

What about a Poisson regression? I created a data frame containing your data, plus an index t for the time (in months) and a variable ...
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  • 12.1k
12 votes
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Why is stl function giving significant seasonal variation with random data

Loess decomposition is intended to smooth the series by applying averages to the data so that it collapses into components, e.g. the trend or seasonal, that are interesting for the analysis of the ...
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  • 11.3k
11 votes

Does a seasonal time series imply a stationary or a non stationary time series

A seasonal pattern that remains stable over time does not make the series non-stationary. A non-stable seasonal pattern, for example a seasonal random walk, will make the data non-stationary. Edit (...
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  • 11.3k
11 votes
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Seasonal adjustment a la Hyndman

First, the model involves additive seasonality. It is not complicated -- just a simple Fourier approximation to the seasonal term. Yes, the original post missed the subscripts on the coefficients; the ...
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  • 52.9k
11 votes

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

A glance at the manual for auto.arima shows that an explanation of precisely why it found the solution it did in this case would be complicated: depending on the ...
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10 votes
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very high frequency time series analysis (seconds) and Forecasting (Python/R)

Question #1: The problem is that in the MLE case, both the Python (statsmodels) and R procedures use state-space models to estimate the likelihood. In an SARIMAX class, the state-space grows linearly ...
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  • 1,243
10 votes
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Seasonality not taken account of in `auto.arima()`

(First off, cmort is already a ts object with frequency 52, so you don't need to coerce it.) ...
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9 votes
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What's wrong to fit periodic data with polynomials?

In just the dataset you've provided, the only real downside to using polynomials over the Fourier basis is the issue of discontinuity at $T = 0$ and $T = 24$. As you stated, you can add constraints to ...
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  • 18.3k
9 votes
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Seasonal data deemed stationary by ADF and KPSS tests

Both the augmented Dickey-Fuller (ADF) test and the Kwiatkowski, Phillips, Schmidt and Shin (KPSS) test are tailored for detecting nonstationarity in the form of a unit root in the process. (The test ...
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9 votes

Do I have to add the seasonal effect and trend back to ARIMA forecast?

No, you do not need to remove trend and/or seasonality before fitting an ARIMA model. These models can handle certain types of trends and certain types of seasonality by themselves, or by including ...
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  • 5,499
9 votes

Time series seasonality test

Before you test for seasonality you should reflect which type of seasonality you have. Note that there are many different types of seasonality: Additive vs. Multiplicative seasonality Single vs. ...
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  • 4,963
9 votes
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Searching for a weekly rhythm in weight loss/gain

Using differences between succeeding days (more susceptible to noise) Compute for every week $i$ the seven values $$\begin{array}{rcl} d_{1i} &=& weight_{Monday}-weight_{Sunday} \\ d_{2i} &...
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8 votes
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SARIMA model equation

Excerpt from a comment clarifying the actual confusion: I always found it a odd way to define the model. Consider the SARIMA(1,0,0)(1,0,0)24... isn't this the same as the much simpler rendering $...
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8 votes
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Why should we remove seasonality from a time series?

Burman, J. Peter (1980), “Seasonal Adjustment by Signal Extraction,” Journal of the Royal Statistical Society, Series A, 143, p.321 The reasons according to Burman: The most common is to provide ...
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  • 56.8k
8 votes
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Forecast daily data with weekly and monthly seasonality using exponential smoothing

To the best of my knowledge you cannot use exponential smoothing for daily forecasting that involves irregular seasonal effects or causal variables like holidays. The paper you cite is requires well ...
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  • 7,479
8 votes

Is this an appropriate method to test for seasonal effects in suicide count data?

A chi-square test is a good approach as a preliminary view to your question. The stl decomposition can be misleading as a tool to test for the presence of ...
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  • 11.3k
8 votes
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Why is my design matrix rank deficient? (modelling seasonal data with a cyclic spline)

cyclicSpline already contains the constant vector in its span so if you additionally add an intercept it'll be rank deficient. ...
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  • 18.8k
7 votes

ARIMA SARIMA model mathematical formula

Writing the model using operator polynomials $$ \phi(B)\Phi(B^{12})y_t = \theta_0 + \theta(B)\Theta(B^{12})e_t $$ that is, for an ARIMA$(1,0,4)\times(2,0,2)_{12}$ process, the model is $$ (1-\phi_1B)(...
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  • 8,627
7 votes
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How to identify the seasonality of a timeseries from the Periodogram?

Well, the periodogram after taking first differences doesn't indicate any clear periodicity. However, be aware that taking first differences amplifies high-frequency components, which should appear in ...
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  • 3,019
7 votes
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Deseasonalizing data with fourier analysis

The term you're looking for is "trend and seasonality decomposition of time series". Google this. There are many approaches. If you really have only 100 points then Fourier will not work very well. ...
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  • 56.8k
7 votes
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stl() gives seasonal component, but ets() and auto.arima() choose nonseasonal models

Let's load your data (this is why dput is useful): ...
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7 votes
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Time series data with seasonality using VAR?

VAR models are routinely used with seasonal data, e.g. in macroeconomics where most of the time series (such as GDP or unemployment) are seasonal. Seasonality is handled either (1) outside of the ...
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7 votes
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Error while fitting data in auto.arima - R

This warning (not an error) is informing you that the seasonal unit root test (used to select the number of seasonal differences, D) has errored. Admittedly, the message is not very informative for ...
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7 votes

Can you suggest a novice method for detrending and deseasoning time series to find relationship between two variables?

I wanted to expand on my comment: So let's simulate a series which exhibits a basic trend, seasonality, and reacts to an exogenous variable. (I am working in python) ...
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  • 1,365
6 votes

Is this an appropriate method to test for seasonal effects in suicide count data?

As noted in my comment, this is a very interesting problem. Detecting seasonality is not a statistical exercise alone. A reasonable approach would be to consult theory and experts such as: ...
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  • 7,479

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