An Econometric Time Series Model Analysis: Textile Sales in Japan 1995-2014
School of Economics, University of Sydney
ECMT6003
Applied Business Forecasting
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Date?
Abstract
This project uses time series analysis techniques to elaborate its significance as an analysis and forecasting tool in the econometric space. It analyzes the variations and changes in seasonality in a textile firm’s sales output in Ottawa, Japan, over two decades. The monthly net sales of fabric and textiles are recorded from January 1995 to December 2014. The data was sourced from the R Console database for analysis and forecasting needs. In this short study, three key factors are investigated, and conclusions are drawn based on their response to the available data. First off is the fluctuation of the volume of textile sales over 20 years. Seasonal effects on the production and consumption of textile products were also investigated. Lastly, the most important of all is the forecast for the company’s volume of textile sales over the next four years. Performances by the chosen ARMA model are verified based on appropriate statistical analysis and prediction. By applying the predictive models proposed by this study, the textile company stands to enjoy the liberty of adjusting to future market uncertainties due to changes in seasons and planning appropriately to maximize profits both in the short run and in the long run. In the concluding part of the study, prospective issues about sales projection and its impact on the textile industry are discussed, and a few suggestions for future studies.
Key terms
ARIMA model, Stationary, Box-Jenkins procedure.
Introduction
Japan’s renowned textile expertise, exquisite and creative fabric design, innovative mass production, and unparalleled technology advances are at a turning point in the early twenty-first century. During the past few decades, market forces such as high labor and inflation costs have led to massive import of fabrics to the neighboring Asian countries, especially China, and increases in importing fibers and materials. This is a condition well known to other major industrialized fabric-producing countries. However, Japan’s case is particularly poignant, given its rapid rise to preeminence and its scientific advances in fiber, fabric, and apparel making. Recent generations of Japanese fashion designers and fabric creators, often in collaborations, have realigned aesthetic paradigms to wide international acclaim by showing daring new clothing construction in fabrics that seemingly defy gravity and previous performance and appearance limits.
Like most indispensable sectors in the economy, Japan’s textile industry poses a significant income earner for an economy. In the last two decades, the fashion industry has made a drastic leap towards ensuring a steady supply of textile products to the ever-growing global market. Textile products are widely used to perform a wide range of undertakings. Through textiles, Japan’s economic boom was witnessed in the late 1900s into the 21st century when the West has become complacent in the sector due to the heightened industrial revolution. Japan boasts a rich range of indigenous textile products, and it is noted that they consume over 60% of its textile products and raw materials locally.
The monthly textile sales data is used to enhance productivity in other related areas of specialization in the economy. The predictive econometric equation is a vital component of making informed decisions on fiscal matters within a company. Textile monthly net sales projections are essential for policymakers to monitor and evaluate the options that would lead to developing a working formula to maximize profit margins within the company. This study focuses on defining the reliability of the Sales model for the textile industry in Japan during this period to address pertinent concerns of forecasting short term projections of sales, identifying and explaining the seasonality of monthly sales and its impact on the general profitability of the textile industry. It further analyzes the time series econometric model of the country’s sales variable in the 20th and 21st Century interface.
Time series are explicitly manipulated through various techniques and tests that have a backing of statistical nature to unravel the basis and why specific data occur the way they do. (Box et al., 1996). Once the reason behind the behavior of data is understood and interpreted, it opens a doorway for researchers to model a formula that replicates the phenomenon at hand. This would then lead to forecasts and analysis being done to solve recurrent problems in the business world. (Yang, 2009).
Most time-series data are usually non-stationary due to the existence of seasonality in them. To make these types of data ready for statistical manipulation, techniques such as differencing and finding the data’s natural logarithm make it stationary and integrated. The Box-Jenkins method is used to find the constants p, d, q, which determines the model of an ARMA. The model parameters are calculated using OLS. In the sections that follow, the techniques responsible for productive modeling models will be discussed in detail. By conducting time series analysis, we aim to understand the basis of variation and seasonality in time series data and why they occur that way and make forecasts on vital data to serve in the business world. We would also like to know and understand how certain separate events influence these fluctuations in the data (Brockwell and Davis, 2002)
Methodology, Collection, and Summary of data
The time series analysis methodology involves molding a model to explain the essence of how time series data comes about and to also predict future observations on data.
Y(j) = k1 + k2Y(j-1) + k3X(j-1) + ej,
X(j-1) and Y(j-1) are the inputs and the outputs, in that order.
Autoregressive processes as their name implies, regress on themselves. If an observation made at time (t), then, p-order, [AR(p)], autoregressive model satisfies the equation:
X(j) = A0 + A1X(j-1) + A2X(j-2) + A2X(j-3) + . . . . + ApX(j-p) + ej,
where ej is a White-Noise series.
The series is a linear combination of the last few series’ last values, including an error term, that integrates something new in the series at time t that is not clarified by past data points. It resembles a multiple regression formula, except it is regressed to last observations instead of the regular independent variables.
Box-Jenkins methodology
There are a few necessary steps to follow when using this technique to identify, select, and assess econometric models for time series data. They are discussed below.
Time series stationarity. When it reaches a time where the variance of a time series data equals the mean of the same data, then that moment is considered a stationary point of a time series. Typical Box-Jenkins ARMA models exclusively perform well with stationary time series.
The stage and the parameters for estimation must be specified as a requirement.
Forecasting: Upon checking the goodness of fit and the predictive ability, a model can generate dummy observations that follow a specific pattern parallel to the real observations.
By choosing to use the ARIMA method explicitly to define time series data fully, the AR part in ARIMA is assigned p, d is given to the integrated factor, and q assigned to MA. AR is the outcome of the last observations. The I component represents trends (Boshnakov,2016). For a model to work effectively, all three elements must be put in the command without fail.
Collection of Textile Sales data
The total net monthly textile sale equals the total amount of revenue collected from selling textile products both finished and unfinished less the running and the production expenses. This also includes corporate tax obligations. These figures are in millions of dollars, thereby giving a vivid picture of how business in the textile industry flourished.
The annual percentage sale of textile products and other related products is made entirely through the Japanese Yuan. Comparisons are made using the US dollar. As pointed out by the World Bank, the Net annual textile sales in Japan were worth 27.22 billion US dollars in 2011. This accounts for 0.03% of the global economy. Through the 1960s, Japan’s textile exports were profitable. However, its market share was already then beginning to suffer from lower-wage competition from Hong Kong, Korea, and Taiwan, the so-called Newly Industrializing Economies (NIE). The acrimonious 1969-72 Japan-U.S. textile negotiations were followed by steep increases in raw materials, labor, and fuel costs, amid growing competition from the NIE. Japanese companies responded by developing new, value-added high-technology products and equipment. In an inversion of events at the beginning of the century, they entered into agreements to share their patents and licenses with NIE countries. Through the last quarter of the twentieth century, Japanese companies launched innovative products embracing Kansei concepts. Many have already become commercially successful, and others are mainstays in projects for sustainable development.
Data Summary
The data was obtained from the R console database, and this data was converted to time series data through a series of commands. Because of this data’s univariate nature, there was little preparation of the data regarding cleaning and filtering the unwanted data. The information was then viewed in the R consoles output window, and a summary of the data obtained. The following is our time series data illustration from the analysis software.
Figure 1: An illustration of the monthly textile sales in Japan over a time
The data was then plotted for visualization. The diagram below shows the resulting plot.
Figure 2: A plot showing the fluctuation of Sales over a time
Figure 3: A boxplot of Sales over a time
From the foregoing, by empirical analysis, it can be noted that the data from the sales were over time series data and that it clearly shows the seasonality and variation of textile sales over time for twenty years, which means that the data is non-stationary. Nonetheless, from the above two illustrations, we can note a few observations before delving deeper into the advanced analysis. It is seen that the yearly trend shows that the amount of sales has been increasing without fail. This is explained by the upward trend taken by the graph. Additionally, the variance and the mean sales amounts in June and December are higher than all the other months. Although the mean value of each month differs, their variance is relatively small. Therefore, we can confirm the presence of a strong seasonal effect having a cycle of 6 months.
Data analysis
Here, the monthly textile sales dataset from Ottawa, Japan, which includes the average monthly sales of textiles and its products in millions, will be investigated from 1995 to 2014. Owing to the nature of the non-stationarity of our data, there is a need to remove this attribute to allow us to run a predictive analysis using an appropriate model. There are three ways this can be achieved: By Detrending- involves the removal of the trend from the time series. If I had a model as below:
b(t) = ( mean+ trend * t) + e
Ignore the enclosed segments and construct the model using the other segments of the equation. By Differencing- Here, the terms are subtracted from each other, and the residual used instead of the actual time series data. Doing this smoothens the time series even further. i.e.,
b(t) – b(t-1) = ARMA (p, q)
This is the integration part of ARIMA. Conclusively the parameters are as follows:
p: AR, d: I, q: MA
Lastly, by Seasonality. This may be integrated directly and seamlessly into the ARIMA model. An autocorrelation Function plot is constructed to obtain the (p, d, q) values necessary for forecasting. Using our time series data to obtain non-stationary points, we determined the natural log of all the values in our data set the used the ACF (log(x)), where x is our time series data. The following plot was obtained.
Figure 4: Acf plot of Sales data
The ACF chart’s decay is prolonged, meaning that the sales data is not yet entirely stationary. Another round of differencing is required but this time using the natural logarithms of the data. The command for this is,
> ACF (diff(log(Salesdatats));
This gives us a new autocorrelation plot shown below.
Figure 5: Acf plot of differenced Sales data values.
To achieve stationarity, we differenced two times, thus d = 2, p = 0 and q = 2. Finally, we fit the ARIMA model using the parameters above to obtain our coefficients for the econometric model and allow us to do forecasting of sales. We fitted a seasonal attribute in the ARIMA model then visualized a 4-year forecast alongside actual textile sales data for contrast. Running MA(0,2,2) using R syntax, the following output was obtained but first, we run the command:
> MA(2)_model<-arima(log(Salesdata),c(0,2,2),seasonal=list(order=c(0,2,2),period=12))
> coef(MA(2)_model)
ma1 ma2
-1.99333697 -0.99427658
The proposed econometric model for this data is thus;
Xt = εt -1.993εt-1 – 0.994εt-2
> pred<-predict (MA(2)model, n.ahead=4*12)
> pred1<-2.718^pred$pred
> data<-round (pred1, digits=1)
> data
The forecasted four-year monthly textile sales spanning between January 2015 to December 2018 is as shown below.
We obtain the figure below by extrapolating this four-year predicted sales data onto the original data for justification.
Figure 6: A plot showing an extrapolation of the forecasted textile sales for 2015, 2016,2017, and 2018 using MA(2) model
Interpretation and Analysis
We construct the (ARIMA) model explaining the average monthly textile sales in Japan by the use of the Box-Jenkins technique through a linear equation. Basing values on the parameters analyzed, it was found that the ARIMA (0, 2, 2) is the most accurate model for the dataset. This, in other words, is another form of the MA(2,2) model, which proved to be much more precise and useful. The moving average model was proposed to be the ultimate model. A system of estimating and predicting data is provided, proving helpful to organizations, both governmental and non-governmental.
Using the proposed model, it has been established that sales for textile and its products are bound to continue rising considerably in the next four years. This is an essential aspect of prediction, and econometric forecast as the information available to the industry’s policymakers now have the tools and ability to plan in terms of risk assessment and profit or loss projection in the next four years.
This study’s main focus was to seek to shed light on the nature of the time series data that we had in terms of whether there is the aspect of seasonality, a trend in the data, and whether there could be a forecast of the data in the short run. The analysis has been evident in all these aspects. The sales data has two cycles within its calendar year. This is a cycle of six months in each year. Sales increase in volume during June and December. This might be explained by changes in weather and festive season purchasing power. Additionally, the trend apparent in this data is a positive one, which means that as time progresses, sales of textile products increase subsequently.
Conclusion
Modeling is crafting and developing depictions of the real world. Importantly, we need to understand that the outcome analysis is always accurate due to numerous significant forecasting models and not still the reality of life. As a result, the models should conform to reality and not the other way round. Models cannot be entirely reliable as they say the action is taken only through considerable consideration and contemplation. This will have substantial financial repercussions. The ability to build models demonstrating financial data’s inter-relationship is a core aspect of financial planning and financial forecasting. Models showing an association between measures can is likely to be put into enhancing informed fiscal policies. Using an example, people are more worried about the repercussions of a slowdown in another country on the domestic stock market if it can be seen that there is a mathematically demonstrated originative effect between one country’s economy and the local one. A previously accurate model could lose its validity due to changing circumstances, thereby being an incorrect reflection of facts, thereby negatively impacting policymakers.
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