How to Use Guerreropdf’s Method for Statistical Analysis of Economic Time Series

Statistical analysis of economic time series is a vital tool for understanding the behavior and trends of various economic variables, such as GDP, inflation, unemployment, exchange rates, etc. Statistical analysis can help to identify patterns, test hypotheses, forecast future values, and evaluate the impact of policies or interventions.

However, statistical analysis of economic time series can also be challenging, as it requires a solid knowledge of the theoretical and practical aspects of different models and methods. One of the most popular and widely used methods for statistical analysis of economic time series is the one developed by Víctor M. Guerrero, a Mexican economist and professor at the Instituto Tecnológico Autónomo de México (ITAM).

In this article, we will explain what Guerreropdf’s method is, how it works, and how to apply it to your own data using a free software called R. We will also provide some examples and references for further reading.

What is Guerreropdf’s method?

Guerreropdf’s method is a systematic and comprehensive approach for building and evaluating models for univariate economic time series. Univariate means that we are only analyzing one variable at a time, without considering its relationship with other variables. Models are mathematical representations that try to capture the main features and patterns of the data, such as trend, seasonality, cycles, noise, etc.

Guerreropdf’s method is based on the theory of autoregressive integrated moving average (ARIMA) models, which are a general class of models that can handle different types of data structures and dynamics. ARIMA models are composed of three elements: autoregressive (AR), which means that the current value of the variable depends on its past values; integrated (I), which means that the variable has been transformed to make it stationary (i.e., with constant mean and variance); and moving average (MA), which means that the current value of the variable depends on its past errors.

Guerreropdf’s method consists of four main steps:

Identification: This step involves examining the data visually and statistically to determine its characteristics, such as stationarity, trend, seasonality, outliers, etc. Based on this information, we can select an appropriate ARIMA model that fits the data structure.
Estimation: This step involves estimating the parameters of the selected ARIMA model using a statistical technique called maximum likelihood. This technique finds the values of the parameters that maximize the probability of observing the data given the model.
Diagnostic checking: This step involves evaluating the adequacy and validity of the estimated ARIMA model using various criteria, such as residual analysis, goodness-of-fit tests, information criteria, etc. This step helps to detect any problems or deficiencies in the model and to compare alternative models.
Forecasting: This step involves using the estimated ARIMA model to generate predictions for future values of the variable, along with their confidence intervals. This step also involves evaluating the accuracy and reliability of the forecasts using various measures, such as mean squared error, mean absolute error, etc.

Guerreropdf’s method is a flexible and robust method that can handle different types of economic time series and provide reliable results. However, it also requires some skill and judgment from the analyst to apply it correctly and interpret it wisely.

How to use R for this method?

R is a free and open source software for statistical computing and graphics that can be used to implement Guerreropdf’s method for statistical analysis of economic time series. R has many packages and functions that can help with the different steps of the method, such as data manipulation, visualization, modeling, testing, and forecasting.

One of the most useful packages for time series analysis in R is the forecast package, which provides many tools and methods for fitting and evaluating ARIMA models, as well as other types of models. The forecast package also includes the auto.arima() function, which automates the process of selecting the best ARIMA model for a given time series using a variation of the Hyndman-Khandakar algorithm. The auto.arima() function can handle both seasonal and non-seasonal data, as well as external regressors.

To use R for Guerreropdf’s method, we need to follow these steps:

Load the data into R and convert it into a time series object using the ts() function. Optionally, we can also plot the data using the plot() function to get a visual overview of its patterns and irregularities.
Use the tsclean() function from the forecast package to remove any outliers or missing values from the data. Alternatively, we can use other methods such as interpolation or imputation to deal with missing values.
If the data shows a strong growth trend, we can take a logarithm of the series using the log() function to help stabilize it. We can also use the diff() function to apply manual differencing if needed.
Use the decompose() or stl() functions to decompose the data into trend, seasonal, and remainder components. We can plot the decomposition using the plot() function to examine each component separately. We can also use the seasadj() function to obtain the seasonally adjusted series by removing the seasonal component.
Use the adf.test() function from the tseries package to test for stationarity of the series using the Augmented Dickey-Fuller test. If the p-value is less than 0.05, we can reject the null hypothesis of a unit root and conclude that the series is stationary. Otherwise, we need to apply differencing until we obtain a stationary series.
Use the auto.arima() function from the forecast package to fit an ARIMA model to the series. We can specify various arguments to control the model selection process, such as maximum order, seasonal period, external regressors, etc. The function will return an object of class “Arima” that contains information about the fitted model, such as coefficients, variance, log-likelihood, etc.
Use the checkresiduals() function from the forecast package to check the residuals of the fitted model. This function will plot the residuals, their ACF and PACF, and perform a Ljung-Box test for autocorrelation. The residuals should show no patterns or correlations and follow a normal distribution. If there are any problems with the residuals, we may need to modify or compare alternative models.
Use the forecast() function from the forecast package to generate forecasts for future values of the series using the fitted model. The function will return an object of class “forecast” that contains information about the forecasts, such as point estimates, prediction intervals, accuracy measures, etc. We can plot the forecasts using the plot() function to visualize them along with historical data.

The following code shows an example of how to use R for Guerreropdf’s method using a sample dataset of monthly sales of shampoo products:

# Load packages library(forecast) library(tseries)


# Load data

data <- read.csv("shampoo.csv")

data <- ts(data$Sales, frequency = 12)
# Plot data

plot(data)
# Clean data

data <- tsclean(data)
# Take logarithm

data <- log(data)
# Decompose data

decomp <- stl(data, s.window = "periodic")

plot(decomp)

data_sa <- seasadj(decomp)
# Test for stationarity

adf.test(data_sa)
# Fit ARIMA model

fit <- auto.arima(data_sa)

summary(fit)
# Check residuals

checkresiduals(fit)

# Forecast future values fc <- forecast(fit) plot(fc)

Examples of economic time series that can be analyzed with this method

There are many examples of economic time series that can be analyzed with Guerreropdf’s method, as long as they have enough historical data and show some patterns or dynamics over time. Here are some examples of economic time series from different domains and sources:

Gross domestic product (GDP): This is a measure of the total value of goods and services produced by a country or region in a given period of time. GDP is often used as an indicator of economic growth and development. GDP data can be obtained from various sources, such as the World Bank , the International Monetary Fund , or national statistical agencies.
Inflation: This is a measure of the general increase in the prices of goods and services over time. Inflation affects the purchasing power of money and the cost of living. Inflation data can be obtained from various sources, such as the Consumer Price Index (CPI) , the Producer Price Index (PPI) , or the Harmonized Index of Consumer Prices (HICP) .
Unemployment: This is a measure of the proportion of people who are willing and able to work but cannot find a job. Unemployment affects the income and welfare of individuals and households, as well as the aggregate demand and output of the economy. Unemployment data can be obtained from various sources, such as the Bureau of Labor Statistics , the International Labour Organization , or national statistical agencies.
Exchange rates: These are the rates at which one currency can be exchanged for another. Exchange rates affect the competitiveness and profitability of international trade and investment, as well as the value and stability of domestic currencies. Exchange rate data can be obtained from various sources, such as the Federal Reserve Bank , the European Central Bank , or national central banks.
Stock prices: These are the prices at which shares of companies are traded on stock markets. Stock prices reflect the expectations and sentiments of investors about the performance and prospects of companies, industries, and economies. Stock price data can be obtained from various sources, such as Yahoo Finance , Google Finance , or national stock exchanges.

These are just some examples of economic time series that can be analyzed with Guerreropdf’s method. There are many other types of economic time series that can be relevant for different purposes and contexts, such as interest rates, wages, consumption, investment, trade, productivity, etc.

Conclusion

In this article, we have introduced Guerreropdf’s method for statistical analysis of economic time series, which is a systematic and comprehensive approach for building and evaluating ARIMA models. We have explained what ARIMA models are, how they work, and how to apply them to economic data using R. We have also provided some examples of economic time series that can be analyzed with this method.

Guerreropdf’s method is a useful and flexible tool for understanding and forecasting economic phenomena that vary over time. However, it also requires some skill and judgment from the analyst to apply it correctly and interpret it wisely. We hope that this article has given you some insights and guidance on how to use this method for your own data and purposes.

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How to Use Guerreropdf’s Method for Statistical Analysis of Economic Time Series

What is Guerreropdf’s method?

How to use R for this method?

Examples of economic time series that can be analyzed with this method

Conclusion

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