# Forecasting the movement of growth, income & value stocks using ARIMA

Stock markets inherently carry uncertainty, leading to risks. Investors, therefore, use statistical models to predict the movement of a stock before investing, so that their returns can be maximized. The previous article examined the nature of the dataset for growth, income, and value stocks over the period 2000 to 2020 using the ARIMA model. ARIMA helped predict the movement of the average closing price and average return. This article creates the optimal model and predicts the performance of different categories of stocks for the next 10 years i.e. from 1st April 2020 to 31st March 2030. Herein, the selection of the optimal model from the stocks is done based on the value of **average returns (AR)** and *moving average (MA)* coefficients, significance level, and value of AIC and BIC. The rules for determining the model at a 5% or 10% level of significance level are stated below.

- The value of the majority of AR and MA coefficients at different lags should be significant.
- The optimal model should have a minimum value for AIC or BIC.
- The majority of significant values of
**AR**and*MA*coefficient should be less than 1.

A model fulfilling all the above-stated conditions would be selected from the given list of ARIMA models to forecast the performance of growth, income, and value stocks.

The modeling of the time series presents the linkage of the current performance of stocks with the historical data.

## The average closing price of growth stocks using ARIMA

Results of all possible models identified in the previous article** **are shown in Table 1. Herein the cells highlighted in yellow colour depict the coefficients having a p-value of more than 0.05 or 0.10. Based on the 2nd condition, the model (1, 2, 2), (3, 2, 1), and (2, 2, 1) has the least AIC or BIC value. The cells with green colour represent the coefficient value of AR and MA wherein the lag is significant and has a coefficient value of less than 1. However, the identified models (1, 2, 2) and (3, 2, 1) has an absence of significant and less than 1 **AR** and *MA* coefficient but model (2, 2, 1) has their **AR** and *MA* coefficient value significant as well as less than 1. Thus, the ARIMA model (2, 2, 1) is the optimal model for the average closing price.

Based on the coefficient values, the model can be written as

Where Y represents the average closing price and shows the error term of the model.

The determined model is used for the prediction of the future performance of the average closing price. Herein, the average closing price shows that over time there has been a reduction in the closing price value of the growth stocks as the value has decreased from 1052.874 in FY 2019 to 781.2488 in FY 2020. With a slight recovery in FY 2021, there would again be a decrease in the performance of growth stocks. This examination of growth stock’s closing price further is shown in Figure 1.

Financial Year | Annual Average Closing Price |
---|---|

2018 | 1074.216 |

2019 | 1052.874 |

2020 | 781.2488 |

2021 | 807.8962 |

2022 | 799.9501 |

2023 | 826.5974 |

2024 | 808.1012 |

The above figure shows that there would be high variation in the performance of growth stocks but the upward trend is seen in the year 2024 wherein investors would have an opportunity to gain by investing in growth stocks.

## An average return of growth stocks using time series modeling

Based on the possible ARIMA models of average return, the comparison is shown in Table 3. Herein, the assessment of AIC or BIC shows the model (5, 0, 1) and (1, 0, 1). However, in these models majority of **AR** and *MA* are insignificant i.e. 3 **AR** insignificant out of 5 lags. Thus, they cannot be considered as the optimal model. As (1, 2, 1) and (3, 2, 1) have a majority of their coefficient as significant and less than 1, but among them, model (3, 2, 1) has the least AIC or BIC value. Thus, (3, 2, 1) is the optimal model for predicting an average return of growth stocks.

The average return model based on the coefficient values is shown in below table

Where Y represents the average return of growth stocks and shows the error term of the model.

The selected model of average return predicts the **AR** values shown in Table 4. Herein, the **annual average (AR)** return shows that there has been a reduction in earning opportunities for the investors as the return value has decreased from -0.00156 to -0.00178. Though from FY 2022 there has been a slight improvement in the performance by rising in average return to -0.0018 but by FY 2024, again the growth stocks return has decreased. Further, an assessment of the earning opportunity for investors is shown in Figure 2.

Financial Year | Annual Average Return |
---|---|

2018 | -0.00179 |

2019 | -0.00156 |

2020 | -0.00178 |

2021 | -0.0023 |

2022 | -0.0018 |

2023 | -0.00164 |

2024 | -0.00213 |

Figure 2 below shows that there has not been much increase in the earning opportunities for the investors as witnessing the constant change, there is an absence of any trend in the dataset. Thus, despite the high average closing price after FY 2024, the earning opportunity for investors would not increase.

## The average closing price of income stocks using ARIMA

As per the ARIMA models identified in the previous article** **the comparison of the models is shown in Table 5. Herein, the model (2, 2, 1) and (3, 2, 1) are the ones having the least AIC or BIC values. Herein, the model (2, 2, 1) has the majority of the **AR** and *MA* coefficients significant and lesser than 1. Thus, the optimal model for the average closing price of income stocks is (2, 2, 1).

As per the coefficient values, the ARIMA model could be stated as

Where Y is the average closing price and represents the error term of the model.

Based on the model stated in equation 3, the prediction about the annual average closing price is made which is shown in Table 6. Herein, the value depicts that there has been a drastic fall in the average closing price of stocks post-2019 i.e. from 686.2885 in FY 2019 to 357.3055 in FY 2020. These values were further reduced to 157.4541 in FY 2021 but after FY 2022, the closing price has improved to 246.1534. Though there has been slight performance improvement initially, since FY 2024, again, there has been a decline in the value of income stocks. Trend based assessment of income stocks’ closing price is shown in Figure 3.

Financial Year | Annual Average Closing Price |
---|---|

2018 | 843.416 |

2019 | 686.2885 |

2020 | 357.3055 |

2021 | 157.4541 |

2022 | 246.1534 |

2023 | 342.6272 |

2024 | 305.5574 |

The below figure shows that there would be a sharp decline in the closing price of income stocks after FY 2019. Although by FY 2022, the performance would improve, the closing price would be low showing a presence of a downward trend, depicting a decline in earning opportunities for income stock investors.

## An average return of income stocks using ARIMA

Based on the possible models derived in the previous article the assessment of each of the models is shown in Table 7. Herein, model (3, 0, 16), (4, 0, 16) and (3, 0, 3) has the least AIC or BIC values.

The ARIMA model for average return can be formulated as follows:

Wherein, Y represents the average return of income stocks while showing the error term of the model.

The prediction of the average return for income stocks based on the model defined in Equation 4 is shown in Table 8. With an annual average return value of -0.00421 for income stocks, there has been a rise in earning opportunities for the investors to -0.00182. But by FY 2022, the performance of stocks again declined. The return value could be decreased to -0.00174. Thus, there has been variation in the performance of income stocks but still, comparison with growth stocks shows that investors have more opportunity of earning due to higher return earning possibility in growth stocks.

Financial Year | Annual Average Return |
---|---|

2018 | -0.00224 |

2019 | -0.00421 |

2020 | -0.00182 |

2021 | -0.00159 |

2022 | -0.00174 |

2023 | -0.00152 |

2024 | -0.00249 |

Assessment of annual average return shows that initially there has been a negative value of return but after FY 2024, investors would have the possibility of earning a better return. Initially, growth stocks show better earning opportunities as most of the annual average return value of income stocks is below 0. But after FY 2024, income stocks would be a secure source of investment due to the presence of less variability below 0 compared to growth stocks wherein, huge fluctuations could be witnessed.

## The average closing price of value stocks using ARIMA

Based on the identified possible ARIMA models in the previous article, the comparison of all the models is shown in the below table. Herein, the least value of AIC or BIC is for the model (1, 2, 1). With significant and less than 1 coefficient values for **AR** and *MA*, the model (1, 2, 1) is considered an optimal prediction model for the average closing price.

As per the derived model of average closing price, the mathematical form of the model could be stated as

Wherein, Y shows the average closing price of the model while denotes the error term.

Further, the prediction of the average closing price values for value stocks is shown in Table 10 below. Herein, having the value of 132.919 in FY 2019, the closing price would witness a drastic decline in performance i.e. to 48.60683 in FY 2020. This declining performance for value stocks would improve in FY 2022. Detailed examination of the performance is shown in Figure 5.

Financial Year | Annual Average Closing Price |
---|---|

2018 | 184.7788 |

2019 | 132.919 |

2020 | 48.60683 |

2021 | 46.06175 |

2022 | 62.99034 |

2023 | 121.2559 |

2024 | 152.2917 |

Trend shown in the below figure depicts that compared to the trend of growth and income stocks, value stocks would witness a rise in their performance by having a possibility of an upward trend. But despite this upward trend, the closing price value estimation would be less than the growth and income stocks value. Thus, value stocks investors due to the upward moving trend would have an opportunity of earning higher returns due to rising closing prices but this value would be less than income and growth stocks.

## Average return of value stocks using time series modeling

The comparison of all identified ARIMA models for average return in the previous article is shown in Table 11. Herein, the assessment of AIC or BIC value shows that models (3, 0, 12) and (5, 0, 12) have the lowest values. However, for the model (3, 0, 12) majority of **AR** and *MA* coefficient values is insignificant and even more than 1. Thus, it would not be the optimal model for predicting the performance of average return. As, model (5, 0, 12) has a majority of coefficient values as more than 1 and significant, thus, (5, 0, 12) is the efficient and optimal model for average return.

Based on the identified ARIMA model, the mathematical form of the model is stated below.

Where Y shows the average return of the model while depicts the error term.

The prediction of the annual average return is further shown in table 12 below. Herein, the value of the return is -0.0059 for FY 2019 which has decreased to -0.00248 in FY 2020 showing the availability of earning opportunities for the investors of value stocks. There has been a reduction in earning possibility for investors with the availability of decreasing possibility in future. As the value of the return is negative, there is the possibility of loss in future which is even higher than the income and growth stocks loss probability. A detailed assessment of the performance is shown in Figure 6 shown below.

Financial Year | Annual Average Return |
---|---|

2018 | -0.00357 |

2019 | -0.0059 |

2020 | -0.00248 |

2021 | -0.00256 |

2022 | -0.00302 |

2023 | -0.00301 |

2024 | -0.00291 |

The below figure shows the prediction of average return movement for the next 10 years. Herein, in presence of high fluctuations, the return earning possibility is less as majorly the trend value is below 0. Comparing the performance with the income and growth stocks, the analysis shows that investors of value stocks have more probability of loss in the longer term.

## Overall stocks’ performance in the Bombay Stock Exchange

To optimize returns on stock market investments, forecasting stock price trends is important. In this study, 303 stocks listed in the Bombay Stock Exchange for the period 2000-2020 were analysed. These stocks were split into three types:

- growth,
- income and,
- value stocks.

The prediction of stock performance in this study states that the growth stocks offer a maximum earning possibility for investors. Although there is the presence of variation, the majority of the annual average return is above 0. Therefore, the investors would still benefit from this stock. Income stocks are secured investments, therefore provide less earning possibility in comparison to growth stocks. However, the amount of inherent risk is also less. Thus, there is a huge variation in the average return for income stocks at the level above and below 0 value. However, in the longer term due to the upward focused trend, there is the possibility of a safe return for investors.

Value stocks are a source of risky investment. With the majority of annual average return values below 0 levels, the investors of these stocks would bear the loss and this possibility rises in longer term as the trend is focused on negative values. Hence, investors seeking more returns should invest in growth stocks, but investors who prefer more secure investment should opt for income stocks.

#### References

- Jampala, R. C., Goda, P. K., & Dokku, S. R. (2019). Predictive analytics in stock markets with special reference to BSE Sensex.
*International Journal of Innovative Technology and Exploring Engineering*,*8*(6), 615–619. https://doi.org/10.35940/ijitee.F1127.0486S419 - Perwej, Y., & Perwej, A. (2012). Prediction of the Bombay Stock Exchange (BSE) Market Returns Using Artificial Neural Network and Genetic Algorithm.
*Journal of Intelligent Learning Systems and Applications*,*04*(02), 108–119. https://doi.org/10.4236/jilsa.2012.42010

## Discuss