Autoregression by Udny Yule, Eugen Slutsky
In 1927, Udny Yule and Eugen Slutsky independently introduced the notion of autoregression, a type of regression where the variable of interest is regressed on its own lagged values. This concept has since been widely used in statistics and econometrics. In this paper, we review the history and development of autoregression from its origins to the present day.
We begin with a discussion of Yule’s original work on time series analysis and his proposal of using autoregression to model such data. We then turn to Slutsky’s contribution, which was to formalize the idea of an AR process and to develop estimation methods for this type of model. Next, we consider some more recent developments in the theory and applications of autoregression.
Finally, we conclude with a discussion of some open problems in this area.
In 1927, Udny Yule and Eugen Slutsky independently developed the autoregressive model, which is a stochastic process where each observation is a linear function of past observations. The autoregression model is used to predict future values of a time series based on its past values. It is a type of regression analysis that estimates the coefficients of an equation by minimizing the sum of squared errors.
The autoregression model has many applications in economics, finance, and engineering. For example, it can be used to predict stock prices, exchange rates, interest rates, and energy consumption. The autoregression model is also widely used in signal processing to remove noise from data.
There are several advantages of the autoregression model over other forecasting methods. First, it is simple to understand and implement. Second, it does not require extensive data preprocessing or feature engineering.
Third, the autoregression model can be easily extended to multiple time series (multivariate autoregression) or non-linear models (non-linear autoregression).
Despite its simplicity and flexibility, the autoregression model has some limitations. First, it assumes that the data are stationary, meaning that they do not change over time.
This assumption may not hold in practice; for example, stock prices typically exhibit non-stationary behavior due to trends such as bull markets and bear markets. Second, theautoregressivemodel only uses information from the past; it does not incorporate information about future events that may impact the time series (such as earnings announcements). Finally, the predictions made by theautoregressivemodel are often inaccurate when there are large changes inthe data (such as structural breaks).
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What is the Slutsky Yule Effect?
In economics, the Slutsky–Yule effect is a logical relationship between two seemingly unrelated economic phenomena. The Slutsky effect is named after Eugen Slutsky who first published it in 1915 while the Yule effect is named after George Udny Yule who first published it in 1926.
The Slutsky effect states that when income increases, consumption will also increase.
However, the amount that consumption increases will be less than the amount that income increased. The Yule effect states that when income decreases, saving will increase. Again, the amount saved will be less than the amount of income lost.
What is the Meaning of Slutsky?
In economics, Slutsky is an important concept used to understand consumer behavior. It is named after Russian economist Eugen Slutsky. Slutsky decomposes the change in demand for a good or service into two distinct effects: the substitution effect and the income effect.
The substitution effect occurs when the price of a good or service changes and consumers respond by substituting away from the more expensive option. For example, if the price of steak increases, consumers may choose to purchase chicken instead because it is cheaper. The income effect occurs when a change in price affects consumers’ real incomes and they respond by changing their consumption accordingly.
For example, if the price of gasoline decreases, consumers may choose to drive more because they can afford it.
Slutsky is important because it allows economists to analyze how changes in prices will affect both what consumers buy (substitution effect) and how much they consume (income effect). This information can be used to make better policies that improve welfare and optimize economic outcomes.
Who was Slutsky in Economics?
Lev Slutsky (1881-1948) was a Russian economist who made important contributions to the study of consumer demand and producer theory. He is best known for his work on substitution and income effects, which are two key concepts in microeconomics. Slutsky also did groundbreaking work on general equilibrium theory and interest rate determination.
Who Invented Autoregressive Models?
In the late 1940s, economists began developing autoregressive models to analyze time series data. These models were originally called “distributed lag models,” but they are now more commonly referred to as AR models. The first AR model was proposed by Yule in 1927, but it wasn’t until the 1950s that economists began using these models on a regular basis.
Some of the early pioneers of AR modeling include Simon Newcomb, Box-Jenkins, and Robert Engle.
AR models are used to predict future values of a time series based on past values of the same time series. For example, an AR model could be used to predict next month’s stock market prices based on this month’s stock market prices.
To develop an AR model, you need to specify two things: the order of the model (p) and the parameters (θ1,…,θp).
The order of the model refers to the number of lags included in the model; for example, if p=2 then your model would use two lags (i.e., Xt−1 and Xt−2). The parameters are estimated coefficients that tell you how much eachlag contributes to predicting the value at time t.
Once you have specified these two things, you can estimate your autoregressivemodel using least squares regression.
Conclusion
Udny Yule and Eugen Slutsky, two of the founders of time series analysis, developed the autoregression model in 1927. Autoregression is a statistical model that uses past values of a variable in order to predict future values of the same variable.
Yule and Slutsky’s work on autoregression was motivated by their desire to find a way to predict future values of economic variables such as prices and production levels.
They found that autoregression was particularly well-suited for this purpose.
The key advantage of autoregression is that it can be used to make predictions even when there is little data available. This is because the model only requires data on past values of the variable being predicted.
Autoregression has been widely used in economics, finance, and other fields since its development by Yule and Slutsky. It remains an important tool for making predictions about future events.
