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Say I have an excel file with format like this (to download from this link):

Note the first column is year and the first row is month.

I try to convert it to time series object then draw a seasonal plot using ggseasonplot or ggplot2.

I use forecast package in R.

Hyndman says:

The arima() function in R (and Arima() and auto.arima() from the forecast package) fits a regression with ARIMA errors.

I have an output for auto.arima()

I have the below time series for weekly fish caught in a specific location (period=52 for weekly data) and only 55 datapoints

I am trying to forecast a time series in Python by using auto_arima and adding Fourier terms as exogenous features. The data come from kaggle's Store item demand forecasting challenge. It consists of a long format time series for 10 stores and 50 items resulting in 500 time series stacked on top of each other. The specificity of this time series is that it has daily data with weekly and annual seasonalities.

In order to capture these two levels of seasonality I first used TBATS as recommended by Rob J Hyndman in Forecasting with daily data which worked pretty well actually.

I also followed this medium article posted by the creator of TBATS python library who compared it with SARIMAX + Fourier terms (also recommended by Hyndman).

But now, when I tried to use the second approach with pmdarima's auto_arima and Fourier terms as exogenous features, I get unexpected results.

In the following code, I only used the train.csv file that I split into train and test data (last year used for forecasting) and set the maximum order of Fourier terms K = 2.

My problem is that I obtain a smoothed forecast (see Image below) that do not seem to capture the weekly seasonality which is different from the result at the end of this article. Is there something wrong with my code ?

Complete code :

Here is my code:

Here is my code:

I have to create demogdata object based on my data. ‘Fert’ and ‘Mort’ objects – rates, exposure – are all clear. But concerning the ‘Pop’ object. I understand it must be population as of Jan 01, not exposure (actually I checked it by comparing raw data from HMD txt files and Hyndman’s original ‘pop2010’ object). But what an argument must I put instead of ‘rates’? What I have tried: 1. put an argument ‘skip’: dnipop <- read.demogdata(file=skip, "pop.txt", ) It’s does not work. 2. put the same data as pop (sort of dummy variable): dnipop <- read.demogdata("pop.txt", "pop.txt", ) Actually, it’s work seamlessly. I managed even to walk through to the completed forecast. But still, I’m curious how to do it correct, without 'rates' element. Example you can find here enter link description here I other words, Hyndman's object has structure:

stR package is based on Hyndman and Dokumentov 2015 and contains an STR() function to which you may provide a description of topology of the seasonality you deal with, which is defined by a list of segments and a list of seasonal knots for each predictor you use (including trend). You may also provide a list of time knots. There is a vignette that is supposed to explain everything via examples, but neither the vignette nor the paper explains what these knots (time and seasonal) and segments are, and I failed to deduce that from the vignette, even though it's quite extensive. So, what are these things? What would they be for a simple model with, say, daily data and only trend + weekday/weekend seasonality? Full disclosure - I haven't looked at the source code yet, but I doubt it would make things more clear for me.

I am trying to use ETS function from fable package (following this tutorial link). Ideally I would like to do it without using tsibble functionality. In particular I am trying to generate forecast: