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I have an msts time series, hourly data of electricity prices that have daily, weekly and yearly seasonality. I am decomposing the data using TBATS. Data I am using covers 365 days.

Residuals have almost zero mean and a normal distribution. However there seems to be some correlation. The data I am using has a lot of spikes with high variance so is this normal? How can I improve the decomposition? How should I evaluate the Ljung Box Test?

Ljung-Box test

data: Residuals from TBATS Q* = 22076, df = 8733, p-value < 2.2e-16

X-squared = 858.16, df = 48, p-value < 2.2e-16

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Electricity prices are driven by external factors that depend on network effects and weather, especially if weather-dependent renewable energy is involved. Your negative prices indicate periods where someone generated too much electricity and needed to offload it - by paying someone else to take it. Things like this happen, e.g., when Germany generates more wind power electricity than it can handle by itself, so it pays neighboring countries to take it off their hands. So you will quite probably need to take weather and similar effects into account.

I strongly recommend that you take a look at Rafal Weron's work on modeling and forecasting electricity load, demand and prices, e.g.,

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Perhaps your data has holiday effects or perhaps week-of-the-month effects or perhaps day-of-the month effects. Perhaps there are pulses in the series. Perhaps the hourly effect differs based upon day-of-the-week . Only the data knows for sure. Perhaps you need 24 distinct models.

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