A time series collects past observations to develop an appropriate model over a regular time interval. A single time series consists of a single variable value taken over periodical times and multivariate time series consists of values taken over a period by many variables in the exact periodic times. Any time-related data that is subject to time can be called time-series. These types of results, patterns, no stages, and seasonality can see on an annual, weekly basis. If any one of these parameters can impede, this form of data is affected adversely. Being a data scientist interested in the study of time series, he/she is now obliged to analyze the data and then use them for sound forecasts to make future predictions. The study of temporal data can give us an accurate picture of how a variable evolves or how it relies on changes in other variable values.

This relationship of a variable with previous values or other variables can be evaluated or predicted in the time series and has many artificial intelligence applications. An appropriate model can prepare on a specific time series in practice, and the respective parameters calculated using the known data values**. **A time-series to be mounted on a correct model is called a time series analysis. It includes methods that try to understand the essence of the series and help future predictions and simulations. Past observations are obtained and analyzed in time series forecasts to create a suitable mathematical template to capture the data generation procedure.

**What is Time Series Forecasting?**

Past observations are collected and analyzed in time series forecasting to build an appropriate mathematics model that captures the data generation process. The events for the future can predict with the model. This method is beneficial if the predictive trend followed by successive observations does not well establish or if the explanatory model is not satisfactory. Time series forecasting in various fields has significant applications. Valuable strategic and precautionary decisions also are made based on the outcomes of the projections.

**Why Forecasting**

Since time series forecasting (e.g., demand and sales) is also precious. The core business strategy, procurement, and development activities drive most manufacturing companies. Any errors in the forecasts can tear through the supply chain or any business context. Therefore, it is necessary to get the projections correct to save costs and to succeed. Time series forecasting is applicable in any business.

**Time-Series Forecasting Models in Python**

- Autoregression (A.R.)
- Autoregressive Moving Average (ARMA)
- Autoregressive Integrated Moving Average (ARIMA)
- Seasonal Autoregressive Integrated Moving-Average (SARIMA)
- Seasonal Autoregressive Integrated Moving-Average with Exogenous Regressors (SARIMAX)
- Vector Autoregression (V.A.R.)
- Vector Autoregression Moving-Average (VARMA)
- Vector Autoregression Moving-Average with Exogenous Regressors (VARMAX)
- Holt Winter’s Exponential Smoothing (HWES)

**Introduction to ARIMA Models**

**ARIMA** (‘Auto-Regressive Integrated Moving Average) is, in fact, a type of model that “explores” a particular series of times based on their values from past times, i.e., their lags and lagged forecast errors, to allow the equation to predict future values. The ARIMA model consists of a series of statistical models for time series analysis and forecasting. The program explicitly includes a set of standard time series data structures, and as such, offers an easy but robust way to predict time series skillfully. ARIMA is an acronym for an integrated moving average of Auto-Regressive. It generalizes the simpler Autoregressive Moving Average and adds to the integration framework. ARIMA model comparison with other models

Model | Pros | cons |

Linear Regression | Ability to handle different time series components and features. High interpretability. | Sensitive to outliers. Strong assumptions. |

Exponential Smoothing | Ability to handle variable level, trend, and seasonality components. Automated optimization. | Sensitive to outliers. Narrow confidence intervals. |

ARIMA (Autoregressive Integrated Moving Average) | High interpretability. Realistic confidence intervals. Unbiased forecasts. | Requires more data. Strong restrictions and assumptions. Hard to automate. |

Source: analyticsindiamag.com

ARIMA acronym describes the main aspects of the model.

**AR: Autoregressive**. The model uses the relationship of observation with many lagging observations.

**I: Integrated**. The use of raw observational differentiation (for example, by subtracting an observation from the previous period) to stabilize the time series.

**MA: Moving average**. The lagged experiments model is the dependence between the observation and a moving average model’s residual error.

Formal ARIMA statements (p, d, q) can use where the parameters can replace by integer values to show the particular ARIMA type used quickly.

The ARIMA model parameters define as:

**p:** Number of lag observations in the model, also known as the lag order.

**d:** The number of differences between the raw observations, also called differentiation degrees.

**q:** Moving average screen size, also referred to as the average moving order

The Standard statements of ARIMA (p, d, q) can use where the parameters can replace by integer values to show quickly the particular ARIMA type used.

A linear regression model, including the number and form of terms defined, is constructed. The data is prepared to make it stationary to eliminate tendencies and the seasonal mechanisms that negatively influence the regression model. The data can compile. A value of 0 can use for a parameter, which shows that the model element cannot use. Thus, the ARIMA model can set up to act as an ARMA model or even as an A.R., I, or M.A. model.

If the ARIMA model can adopt a time series, the observations’ mechanism can produce during an ARIMA process. It can seem clear but may motivate the need to validate the model assumption in the raw observations and residual errors.

**Build ARIMA Model for Time Series Forecasting in Python**

ARIMA estimator can create now. The first phase is to import the library pmd_arima with the Auto_ARIMA feature. In the time series array, the second step is defining a function and returning the Auto-Arima model. These steps show in the following code.

1 2 3 4 5 6 7 8 | import pmdarima as pmd def arimamodel(timeseriesarray): autoarima_model = pmd.auto_arima(timeseriesarray, start_p=1, start_q=1, test="Adf", trace=True) return autoarima_model |

The next phase is to use the above function and build on the training data the ARIMA estimator.

1 2 | arima_model = arimamodel(train_array) arima_model.summary() |

**Output:**

Dep. Variable | D.y | No. Observations | 551 |

Model | ARIMA (1, 1, 0) | Log-Likelihood | -3983.556 |

Method | css-mle | S.D. of innovations | 333.866 |

Date | Wed, 27 May 2020 | AIC | 7973.112 |

Time | 11:37:46 | BIC | 7986.047 |

Sample | 1 | HQIC | 7978.166 |

The above output indicates that the last model was an ARIMA (1,1,0) estimator where the p, d, and q parameter values were, respectively, one and zero. The **auto_arima** functions measure the time series using A.I.C. as a criterion with different combinations between **p,** **d,** and **q.** **A.I.C.** refers to the Akaike Information Criterion, which measures the relative amount of information lost in a particular model. To put it simply, you prefer a lower A.I.C. value. The lowest A.I.C. value for the ARIMA (1,1,1,0) model was achieved in the output above and used as the final estimator.

The first step would be to construct a utility function to be used as an evaluation metric. The following code creates a tool for the calculation of the MAPE error, the to use process. The lower the MAPE, the higher the predictive model performance.

1 2 3 | def mean_absolute_percentage_error (y_true, y_pred): y_true, y_pred = np.array(y_true), np.array (y_pred) return np.mean(np.abs((y_true - y_pred) / y_true)) * 100 |

The following stage is to predict the test data using the below code. The first five findings are printed on the second line.

1 2 | test['ARIMA'] = automodel.predict(len(test)) test.head(5) |

**Output:**

Date | Sales | Class | ARIMA |

01-01-2014 | 6785 | Test | 6882.9 |

01-02-2014 | 6856 | Test | 6889.8 |

01-03-2014 | 6853 | Test | 6898.9 |

01-04-2014 | 6400 | Test | 6907.9 |

01-05-2014 | 6442 | Test | 6916.9 |

The last step is to analyze the test data predictions using the utility function in the following.

1 | mean_absolute_percentage_error (test. Sales, test. ARIMA) |

**Output:**

1 | 9.7846 |

The output indicates that the model result is good.

**Build SARIMA Model for Time Series Forecasting in Python**

Has predicting future events ever crossed your mind? In this technological age, anything is possible.

SARIMA, the most progressive methodology available for use to develop a business plan for any company, from FMCG companies to Automotive companies, can now be combined for forecasting in Python. Seasonal Autoregressive Integrated Moving Average can use for nonstationary data fluctuating modality. Therefore, as long as the data remains the same and does not fluctuate around the same mean, covariance, or variance, you can use SARIMA to identify seasonal and series-related sales.SARIMA or Seasonal ARIMA is the addition of a seasonal data component to the original ARIMA

Using the SARIMA time series forecasting method is supported in Python via the Statsmodels library.

**There are three basic steps in using SARIMA: **

- Define the model.
- Fit the defined model.
- Predict with the fit model.

Take the Key Learnings from each step separately:

**1-Define the Model**

- The training information and a range of model configuration parameters may generate a SARIMAX class case.
- In place of SARIMA, the implementation can name SARIMAX since the “X” extension to the function name also supports exogenous variables.
- These varieties are parallel time series that can not directly model via A.R., I, or M.A. procedures but are available as weighted model inputs.
- An optional “exog” argument can use to specify exogenous variables.
- Trend and seasonal hyperparameters can define as the “order” and “seasonal order” argument in terms of 3 and 4 tuples elements.
- The speed must be these elements
- These are the main configuration elements.

There are other fine-tuning parameters you may want to configure. Learn more in the full API:

1 | statsmodels.tsa. statespace. sarimax. SARIMAX API |

**2.Fit the Model**

- The model can be fitted to the training data once the model can develop.
- The model fits when the fit () function can call.
- The instance of the SARIMAXResults class returns for the model fit is essential. This object includes the data and coefficients, and functions for the use of the model. This object provides information about fit.
- Several fitting elements can configure, and the API should read as soon as the execution is relaxed.

1 | statsmodels.tsa.sarimax.SARIMAX.fit. |

**3.Prediction with Model**

- The model can be used to produce a forecast until it is fit.
- A prediction can call the predict () functions returned from the call fit on a SARIMAXResults item.
- A forecast () function takes a single parameter, specifying the number of time steps for predicting or assuming a one-step prediction if there are no arguments.
- A start and end date, or index, needs to be set to the predict () feature.
- Furthermore, if the model defines exogenous variables, they must also be given to predict function () for the projection duration.

Using machine learning to enable companies to derive product and customer segmentation from forecasting data analysis is invaluable to developing an unbiased and exact Marketing Strategy.

To have technology such as SARIMA and Python combining seasonal and fluctuating data with which to predict sales for FMCG, Automotive, and any other customer-centric market can become the norm in the future. Yes, we might be able to correctly predict the future with these data analytic tools in the hands of the people who know how to develop these technologies correctly!

The SARIMA method model the next step in the series, in line with the differences in the observations, errors, differed seasonal observations, and seasons in the preceding stages. The SARIMA method can use as the linear function of the various observations. It incorporates the ARIMA model to do the same self-regulation, differentiation, and moveable, average seasonal modeling.

1 | from statsmodel.tsa.statespace.sarimax import SARIMAX |

**Time Series Forecasting with Facebook Prophet library in Python**

Several models are available on time series predictive analysis, such as machine learning ARIMA, autoregressive, integrated, moving average model, exponential smoothing, and LSTM. These models need the data to be fed and help us make predictions with some tweaks and fine-tuning. So, wait for the third-party library to exist that can do all the fine-tuning inside and load the model

The Facebook Prophet library answered this question. Facebook introduced it as an API for the projection of time series data-related items. The library is so efficient that it can handle data and seasonal components stationery. We say that by stationary measures, variance and covariance should be constant when dividing data into time and seasonality parts, which implies that the same pattern can follow by the data divided into time intervals.

We can say that:

- The Prophet is a Facebook open-source library that aims to predict univariate time series data automatically.
- How to adapt and use prophet models to produce a sample and out-of-sample forecasts is necessary.
- How can a prophet model be evaluated on an inventory data set?

Let’s say the sales of ice cream in summers are strong and in winter low, and this pattern is followed over the years regardless. Then it’s called seasonal figures. There should be no seasonality and no stationary characteristics over time intervals for data in a time series used as a predictive analysis model. We can use ARIMA, AR, and other models to eliminate the problem of seasonality steps quickly. Still, this problem can solve with the Prophet’s aid. This library provides n parameters for playing and adjusting our model to more excellent performance, e.g., holidays, regular seasonality’s, transformations of Fourier. So, let’s look at this library without taking too much time to implement it with Python’s support.

**Installation**

Make sure that Python/Anaconda and the Pip installation are already in your setup. You should also know how to build a new Anaconda environment to download the libraries with pip or conda. But we’re going to see the setup:

**Step 1:**

One must first install Pystan, the library that helps run Fbprophet, to install Fbprophet. Just open the Prompt or Anaconda Prompt command to install Pystan, and type it.

1 | pip install pystan |

Wait to complete the installation.

**Step 2:**

After Python downloads successfully, the next move is to install FbProphets by piping or conda. Just type under the same command:

1 | pip install fbprophet |

**Step 3:**

When you finish the install and do not make any mistakes, you install the packages effectively and are ready to go on

Run the Prophet facebook library and import in Python. Code below:

1 2 3 4 5 6 7 | # check prophet version import fbprophet # print version number print('Prophet %s' % fbprophet.__version__) |

The example of the Prophet model by using Python on the sales dataset can see below.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | # fit prophet model on the sales dataset from pandas import read_csv from pandas import to_datetime from fbprophet import Prophet # load data path = 'https://raw.githubusercontent.com/jbrownlee/Datasets/master/monthly-car-sales.csv' df = read_csv (path, header=0) # prepare expected column names df.columns = ['ds', 'y'] df['ds’] = to_datetime(df['ds']) # define the model model = Prophet () # fit the model model.fit(df) |

**Conclusion**

For various practical fields, time series modeling and forecasting are essential. Thus, over many years there is a large number of active research work in this area. Many suitable methods for the accuracy and efficiency of time series modeling and forecasting can propose in the literature. This study aims to describe a few ordinary time-series predictions, with their outstanding function, in practice. The proper selection of model orders (for ARIMA), the number of inputs, hidden and output neurons (for ANN), and the constant hyper-parameters (for SVMs) are incredibly critical for good analysis. We addressed the two essential functions, A.I.C. and B.I.C., mainly used to select the ARIMA model. Time-series forecasts are a rapidly growing field of study and thus provide plenty of potential for future work. We have planned, along with other time-series analyses, to find an effective combining model, if possible, in the future.

**References**

- https://www.tutorialspoint.com/time_series/time_series_tutorial.pdf
- G.E.P. Box, G. Jenkins, “Time Series Analysis, Forecasting, and Control,” Holden-Day, San Francisco, CA, 1970
- Lee, “Univariate time series modeling and forecasting (Box-Jenkins Method),” Econ 413, lecture 4.
- J.M. Kihoro, R.O. Otieno, C. Wafula, “Seasonal Time Series Forecasting: A Comparative Study of ARIMA and ANN Models”, African Journal of Science and Technology (AJST) Science and Engineering Series Vol. 5, No. 2, pages: 41-49.
- Cover image credit: www.educba.com