A Comparative Study of Statistical and Deep Learning Model-Base

weather Prediction in Albania

MALVINA XHABAFTI, BLERINA VIKA, VALENTINA SINAJ

Department of Statistics and Applied Informatics,

Faculty of Economy, University of Tirana,

Road “Arben Broci”, Tirana, 1001

ALBANIA

based on water resources. This paper aims to determine the best method for forecasting a natural phenomenon

such as the rainfall, that today in Albania, as a result of the unpredictable flows that it often has, is a major

problem in the field of agriculture. In this study, the rainfall model based on statistical methods, Auto-

Regressive Integrated Moving Average (ARIMA), Error, Trend & Seasonal (ETS) and deep learning models,

Long Short-Term Memory Network (LSTM), and Deep Forward Neural Network (DFNN) was developed. The

study area that will be used for rainfall forecasting is Albania with a time interval between January 1901 and

December 2022. The period that will be used for prediction will be January 2023- December 2024. The

performance of each of the models used has been evaluated by using Root Mean Square Error (RMSE) where

we also used the comparison of training and validation loss curves to analyze and avoid the model overfitting in

the training phase. The results showed that from the comparison between ARIMA and ETS, ETS has the

Received: June 14, 2022. Revised: September 17, 2023. Accepted: October 19, 2023. Available online: November 22, 2023.

1 Introduction

Climate change is an issue that is ranked as a

leading global matter, [1]. It is a very fundamental

factor that affects different sectors of the economy

of a country but in our study, we are going to focus

on the sector of agriculture. Agriculture is one of the

a linear approach that turns natural resources into

products and waste, to sustainable practices that

minimize resource consumption and waste

accumulation, [2]. Also, [1], concluded that the

climate crisis has to shift to a circular production

and consumption model because CE (Circular

Economy) is gaining worldwide attention as a

sustainable alternative for the future. The practice of

predicting weather conditions serves as a way for

agriculture to adapt to the effects of climate change

agricultural production, [3]. In this way, farmers can

make profitable and good choices and also by

utilizing science and technology, the practice of

weather forecasting will foresee forthcoming

atmospheric conditions at a specific location

depending on their needs, [4].

crucial meteorological variables that plays an

consumption, agriculture, pollution, etc. and its

prediction is of great interest, [5]. Besides being

vital to the economy it can seriously damage

infrastructure and crops through floods, [6]. So,

based on the importance of this topic, we will

forecast rainfalls using machine learning algorithms

because are appropriate options for utilization in the

modeling and prognostication of meteorological

events, [5]. This study aims to build a univariate

rainfall time series data model in Albania for the

weather forecasting (rainfalls) impact on agriculture

and management of water and also agriculture in the

transition that is happening nowadays towards

circular economy, and the related work on statistical

and deep learning models we are going to use to

forecast the rainfall time series. Section 3 presents

the study area and the data sets also its main

characteristics, introduces the methods and

algorithms to be used, and also focuses on data and

experimental design. In Section 4 the results are

aforementioned machine learning methods, we

would bring a contribution to the Albanian literature

in this field, since there are few or almost no studies

dealing with this natural phenomenon using this

type of approach.

2 Literature Review & Related Work

Nowadays, climate change is one of the most

current worldwide issues, especially with irregular

predicted to be the foremost influenced sector by

climate change, [7]. Agricultural drainage, rain and

storm runoff, etc. are a consequence of climate

change, which is making it difficult to access water

of a disaster, [9], has become a necessity. Efficient

weather forecasting has the potential to enhance the

agricultural sector's resilience against natural

disasters, minimize damages, steer production, and

enable strategic arrangements for consistent and

increased productivity, [3].

controlled by rainfall allocations, [7], we are going

to focus on forecasting rainfalls as their significance

extends far beyond their role in agriculture as they

sectors, including agriculture, and also plays a

significant role in the circular economy, [11]. On the

other hand, a circular economy has the potential to

mitigate water scarcity issues by directing attention

to water resources used in agriculture and

implementing strategies to reduce consumption and

increase water reuse, [2]. Its implementation can

ensure the conservation of resources, stimulate

agricultural productivity and boost the economy,

[12]. To adopt this approach, the appropriate

is highly crucial to educate and inform the

agricultural industry and its employees about CE's

principles and benefits and its execution needs to be

carried out at the local and why not global level, [2].

Over the past few years, there has been a surge in

the utilization of machine learning algorithms for

simulating atmospheric phenomena due to their

ability to handle large amounts of data, provide a

clear representation of the modeled phenomenon,

and detect patterns or correlations in the data that

aren't readily visible, [5]. In, [7], also stated that the

use of Machine Learning can efficiently handle the

difficulties associated with analyzing extensive

algorithms, to forecast rainfalls. More specifically,

which methods are the best to predict weather

extreme conditions. In, [14], the air quality model

based on the LSTM and ARIMA was developed for

Malaysia on monthly data from the period of 2017–

2019 using air quality data. In, [5], a set of machine

learning methods was used to make predictions

about the phenomenon of rain in the main cities of

Australia in the last 10 years. In, [15], ARIMA and

Artificial Neural Networks (ANN) were used to

forecast monthly rainfall data from year 1901 to

model with a seq2seq structure was introduced to

estimate hourly rainfall runoff. The model was

tested on two watersheds located in Iowa, to predict

24-hour periods of hourly runoff. In, [17], the

LSTM technique was applied utilizing the

meteorological components of Eastern China's

historical information, specifically for the next

twelve hours following a specified time, to improve

the accuracy of rainfall predictions. In, [18], simple

models for estimating rainfall were developed using

using LSTM networks. From 1984

data have been transformed into hourly time series

data. In, [19], two hybrid models utilizing LSTM

networks to accurately predict monthly streamflow

and rainfall patterns were developed. This study

utilized monthly data on streamflow volume

obtained from Cuntan, Hankou, Jinan, and

Wenjiang (Chengdu). In, [6], a rainfall prediction

model with 6 parameters was developed by using

artificial intelligence and LSTM techniques, for

Dhaka city from 2000 to 2014. This study focuses

on developing a system for removing flood damage

LSTM on the time-series data. In this research, two

forecasting precipitation. When making this

decision, one of the factors that is taken into account

is their scores in terms of performance and

accuracy.

3 Tools and Methodology

3.1.1 Study Area

Albania is characterized by a subtropical

Mediterranean climate. The geographical features of

the country are mainly defined by its mountainous

terrain, rolling hills, and coastline, which contribute

method, [22], and the Exponential Smoothing State-

Space model for ETS, [23]. The precipitation

variable has 1464 monthly observations data and the

experiments were carried out using Time-series

Library (R) software.

four hidden layers. In the training phase, the

algorithm uses only 90 percent of the input data

which means that from 1464 examples, only 1392

are used for training and we will keep 36 samples

for validation and 36 samples for testing. These

1392 examples are chosen randomly from the

overall data set. The split of the series is based on

the sequential nature of the data. The first 90 % of

data are used for training and the remaining data are

equally divided and used respectively as validation

after the model is trained, the third set of data is

given to the model and we estimate the out-of-

sample prediction performance. With the results

obtained in this phase, we select the best deep-

learning model. The LSTM and DFNN set aside

10% of the input data for testing and validation and

out of 1464 samples, 36 are used for testing and

another 36 are used for validation.

● Model evaluation and comparison

In this step, we have trained and tested the model

3.2.1 Autoregressive Integrated Moving Average

(ARIMA)

facilitated the construction of an ARIMA model.

The ARIMA model is denoted as ARIMA (p, d, q),

wherein p, d, and q correspond to the number of

autoregressive parameters, degree of differencing,

and the order of moving average, respectively [24].

To be specific, p signifies the autoregressive order,

d denotes the degree of differencing, and q implies

the order of moving average, [22].

(1)

Where, 

3.2.2 Error, Trend, Seasonal (ETS)

The ETS model is utilized to disintegrate a given

series into four distinct components, namely the

level component, the trend component (T), the

seasonal component (S), and an error term (E), [23].

The forecast derived by ETS is generated by

computing a weighted average across all the

observations contained within the time series data

set. The weight values exhibit an exponential

weight to the most recent observation, with the

weights decreasing over observation time, [25].

3.2.3 Long short-term Memory (LSTM)

LSTM is the top deep learning architecture for

future tasks that works with long-range time-series

data by incorporating memory structures to manage

lengthy information and offers solutions for

nonlinear time series, [26]. LSTM was created to

overcome traditional neural networks' inability to

can retain data for an indefinite period, resulting in a

and forget gate. The fundamental concept involves

managing the gate switches by utilizing a non-linear

function to safeguard and regulate the memory unit's

state, and additionally manage the flow of

information, whether it is being amplified or

reduced, [17]. LSTM is one of the most successful

techniques that address the vanishing gradients

effect where they minimize it by implementing three

gates along with the hidden state, [18].

LSTM neural network algorithm exhibits better pred

3.2.4 Deep Feed Forward Network (DFNN)

consisting of a sequence of layers, where

information is directed from the input layer to the

output layer. The architecture of a DFNN model

consists of input, hidden, and output layers where in

the input layer the input vector of a sample is stored

for each iteration while the output layer is the final

stage of the DFNN model where the number of

nodes in this layer is set according to the dimension

of the output data, [27]. The learning process for

DFNN is supervised learning in which the weights,

several interconnected processing units”.

4 Results and Discussions

The analysis of this study is divided into three parts.

The first part is the comparison between the

ARIMA model and ETS. The second part is the

comparison between LSTM and DFNN. The third

part has to do with the comparison of the two best

methods that come out of the first and second parts

38.06956. The ETS model was built and the RMSE

between actual values for variable rainfall in test

data and forecast values found from the ETS model

was calculated. RMSE in this case is 33.89779. The

RMSE and other performance metric values for both

the ARIMA and ETS models are shown in Table 1.

Table 1. Root means square error (RMSE) and other

performance metrics for ARIMA and ETS model

Also, if we have a look at the other metrics shown in

Table 1, for the ARIMA model, they are in larger

values than for the ETS model proving a bigger

error in prediction. Therefore, it could be concluded

that the ETS model can predict rainfall better than

the ARIMA model.

In this part, we will see which of the two deep

followed the steps mentioned in the previous

paragraph “Data analysis”. We have used 2

horizons, 6 and 12 months, and 12, 18, and 24 lags

for each horizon. As a result, we evaluated 6 cases

for each model:

– (LSTM and DFNN) 12-1024-512-256-256-6

– (LSTM and DFNN) 18-1024-512-256-256-12

– (LSTM and DFNN) 24-1024-512-256-256-6

– (LSTM and DFNN) 12-1024-512-256-256-12

– (LSTM and DFNN) 18-1024-512-256-256-6

512-256-256-6 is better than other cases based on

the average RMSE value, of 53.723089. Depending

on the horizon of each model, for horizon 6 the best

model is DFNN 24-1024-512-256-256-6 and for

horizon 12 the best model is DFNN 24-1024-512-

256-256-12. These results are also illustrated in

Figure 2 and Figure 3. Based on the value of RMSE,

the best deep learning model between the LSTM

model or DFNN model to forecast rainfalls in

Albania, is DFNN with horizon 6, lags 24.

Fig. 2: DFNN and LSTM model ranking for

forecasting rainfalls based on the lowest RMSE at

h=6

Fig. 3: DFNN and LSTM model ranking for

forecasting rainfalls based on the lowest RMSE at

h=12

Fig. 4: Training and validation loss for LSTM

Fig. 5: Training and validation loss for DFNN

So, in conclusion, we can say that we evaluated

both algorithms based on the RMSE metric as well

as the best training and validation loss curves from

these two models where the best model in both

comparative cases presented is, DFNN 24-1024-

512-256-256-6.

we came to the conclusion that the two best models

for forecasting based on the RMSE value are ETS

and DFNN models. In this paragraph, we will make

the final comparison if we will use a machine

learning model such as ETS or a deep learning

model such as DFNN for the average rainfall

variable. We will draw this conclusion based on the

performance metrics we have used so far. If we have

a look at the RMSE value for the ETS model which

metric is the ETS model. If we look at Figure 6 and

Figure 7, where the forecast graphs for both models

are presented, the ETS model is closer to the real

values of the average rainfall time series. This

forecast is made for the time interval January 2023 -

December 2024. In Figure 7, we have started the

values from January 2010 to have a clearer view of

the forecast of the values for the years 2023-2024.

agriculture. From the overall information and

comparing the RMSE and observing the

performance of all methods in the comparison for

actual and predicted data, ETS was the one with the

best measurements and results. In other words, the

obtained results illustrate that the statistical methods

optimize the error better than the deep learning

method to see how the result would affect the

current conclusions we have in this paper. Also,

taking into consideration all the variables that affect

References: