A study method for beginners to learn time series analysis
In my personal engineer study session 2019 Advent Calendar, "Introduction to Bayesian Statistics for Statistics Beginners" I wrote an article "How to study until you do" and it was very well received.
So, this time, I would like to write about studying for beginners in statistics to learn time series analysis.
Purpose and target audience of this article
This article aims to help those who have studied the basics of statistics to some extent be able to speak brilliantly on the big topic of "time series analysis" statistics.
The goal of this article is to be able to give you an overview of time series analysis.
Even in time series analysis, the goal is to be able to understand the analysis model called ** state space model **.
The books introduced here are books that you can learn by moving your hands, so knowledge of programming is essential.
What is time series analysis?
What is time series data?
Time series analysis, as the name implies, is a data series that incorporates the concept of time.
The world is full of time series data. I wonder if there is really no data that does not include the concept of time axis! ?? I even think that. Because when you throw the dice 10,000 times (not at that time), the time goes by. However, it is not data in chronological order that tries to ignore the time axis like when throwing dice 10,000 times.
A typical example of time series data is stock prices.
[Nikkei Stock Average wikipedia](https://ja.wikipedia.org/wiki/%E6%97%A5%E7%B5%8C%E5%B9%B3%E5%9D%87%E6%A0%AA% E4% BE% A1)
(I can feel it visually, ** the period of high economic miracle ** ...)
Some people may think that "time series analysis is natural language processing !!". To be sure, natural language processing is one of the most noticeable time series analyzes due to the recent development of machine learning. Everyone "Alexa, what is time series analysis?" When I talked to the stylish cylindrical interior, "Wow, ◯ su !!" The reply is due to the development of natural language processing technology.
However, we do not dare to deal with natural language processing here, only for more general time series data such as stock prices and sales data.
Time Series Analysis Topics and State Space Models
For the big picture of what time series analysis is, This is the book of "Basics of Time Series Analysis and State Space Model: Theory and Implementation Learned with R and Stan". It is described in detail in Mr. Baba's blog logic of blue. (It is no exaggeration to say that the content of this article is all contained in the content of this blog ...)
A state-space model is, very roughly speaking, a type of statistical model that assumes an invisible "state." The observed values are only the results produced from the state. From the state x t </ sub> before the t-1 point, the state x t </ sub> at the t point is generated. The observed value y t </ sub> is generated from the state x t </ sub> at this time t.
In the above Hayabusa (p.179), in the example of fishing, The number of fish in the lake one day is the state, and the number of fish caught on that day is the observed value.
Again, as in this example, it is an observation value with a state. However, since we do not know the state, we have no choice but to guess from the observed values.
Unlike state-space models, so-called general machine learning, it deals with states and observations statistically, so it is a topic of statistics.
It has a certain history, but in recent years it is a statistical model that is often talked about within the framework of Bayesian statistics. (For information on how to study Bayesian statistics, please refer to the article at the beginning.)
Study method
Basics of time series analysis
In time series analysis, the state-space model is a difficult model, not a "classical" method.
As a basis for time series analysis, it is recommended that you first learn "classical" methods such as the ARMA model to get an image.
It is recommended to get a rough atmosphere
The formulas are also easy, so you can read it quickly and get a feel for it.
Grasp the image of the state space model
If you can get a feel for time series analysis, then Hayabusa.
The great thing about Hayabusa is that it explains the image of the state-space model without using mathematical formulas. This is something that great books on statistics and machine learning have in common, but by communicating images in words, the theory that tends to be dry is brought to life.
The explanation of Part 5, which uses the maximum likelihood estimation method for Kalman filter and smoothing, which is the peak of this book, is a masterpiece. Finally, Part 6 also deals with the estimation of state-space models by Bayesian inference.
Hayabusa is also disappointed with Mr. Baba's abstract thinking ability and verbalization ability. I would love to see you once.
A more detailed mathematical understanding of the state-space model
Once you have "completely understood the state-space model" in Hayabusa, let's move on to the hard-boiled mathematical world.
Recommended
It's such a good book that I don't understand why some people give it a low rating. However, it may be a high hurdle for the first state space model. Also, since the story is developed in Bayesian statistics from the beginning, it may be difficult if you are not familiar with Bayes.
If you challenge yourself in a "completely understood" state, you will be taken to the world of "I don't understand anything". However, if you read it back and forth with Hayabusa, you will be able to understand the state space model deeply in the true sense of the word. Looking back at the Kalman filter learned in Hayabusa from the Bayesian statistical standpoint of this book, there is a very deep connection ...
Summary
Time series analysis is a big topic in statistics, but I think it is still an unfamiliar field. The world is so full of time series. Is it because it's difficult?
The key to time series analysis is that the future is created from the past. And the past and the future are somehow similar.
It turns around The times turn around
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