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http://www.dem.umk.pl/dem 

D Y N A M I C  E C O N O M E T R I C  M O D E L S  
DOI: http://dx.doi.org/10.12775/DEM.2017.003  Vol. 17  (2017) 41−57 

Submitted October 2, 2017  ISSN (online) 2450-7067 

Accepted December 17, 2017 ISSN (print) 1234-3862 

Paweł Kaczmarczyk
*
 

Microeconometric Analysis of Telecommunication  
Services Market with the Use of SARIMA Models 

A b s t r a c t. The paper presents the results of testing the effectiveness of the multi sectional 

model in the short-term forecasting of hourly demand for telephone services. The model was 

based on the integration of the linear regression model with dichotomous independent vari-

ables and the SARIMA model. The regression was used as a filter of modelled variability of 

the demand. The SARIMA was applied to model residual variability. The research shows that 

the proposed integration provides a greater possibility of approximation and prediction in 

comparison to the non-supported linear regression model. The results of the study provide 

support for operational planning of telecommunications operator.  

K e y w o r d s: Decision Support System; dichotomous regression; SARIMA model, forecast-

ing. 

J E L Classification: C53; L86; L96.  

Introduction 

 The level of competition in the telecommunication market is getting 

higher. The number of operators is increasing and the division of telecom-

munication markets is increasingly greater. It originated from the execution 

of measures, which were assumed in the Lisbon Strategy (Lisbon European 

Council, 2000) and its current continuation and extension – Europe 2020 

Strategy (Begg, 2010; European Commission 2010). According to these 

strategies the telecommunication market should be primarily liberalised (the 

                                                 
* Correspondence to: Paweł Kaczmarczyk, The State University of Applied Sciences in 

Płock, Faculty of Economic Sciences and Information Technology, 28 Gałczyńskiego Street, 

09-400 Płock, Poland, e-mail: p.kaczmarczyk@pwszplock.pl. 

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Paweł Kaczmarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 41–57 

42 

abolition of restrictions, monopolies and discriminations) and harmonised 

(common regulations to create fair activity conditions for all telecommunica-

tions operators). The premises of the conceptions involve the initiative of the 

Information Society building. 

 In connection with increasingly higher level of competition in the tele-

communications market, the problem of effective modelling and forecasting 

of demand for electronic communication services has gained significantly 

greater importance.  

 Sales forecasts of electronic connection services play a particularly im-

portant role in the management of a telecommunications operator. These 

forecasts support planning policy of the operator, because they are the basis 

for operational planning. Within the framework of operational planning of 

the telecommunications enterprise, decisions relating to price calculation and 

network management are made that are connected with achievement of op-

erational (short and medium-term) objectives. In terms of literature, this 

level of planning is defined as the key decision-making field of managers, 

because the operational planning can strengthen the effectiveness of growth 

of the enterprise value. Due to the fact that operational planning also in-

volves the means to achieve operational objectives, these means may be 

considered as analytical tools. Therefore the use of effective analytical tech-

niques that improve operational management is a source of increase of en-

terprise value. 

 In order to rationalise the operational planning and finally to strengthen 

the market position, managerial staff of telecoms enterprises are interested in 

effective Prediction Systems (PS) application (Dittman, 2004) that belong to 

one of the Decision Support Systems (DSS) subclasses.  

1. The Purpose and Thesis of the Research  

 The literature study leads to statements that PS can function alone, or as 

a part of a broader (multifunction) DSS. The effect of the PS work is the 

prospective information about the external (micro and macro) environment 

of an enterprise as well as internal characteristics of an enterprise. PS is built 

the following components: prognostic database, statistical data pre-

processing methods, statistical data analysis methods, forecasting methods, 

computer programs and forecast monitoring system. 

 Within the framework of the literature on electronic communications, the 

contents, which refer to modelling and forecasting of demand for telecom-

munications services, are not popular. Furthermore, it can be noticed that 

there is a lack of such contents as effectiveness descriptions of the telecom-



Microeconometric Analysis of Telecommunication Services Market… 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 41–57 

43 

munications market data mining techniques and methods (including econo-

metric techniques) applied by operators. It is caused by the existence of the 

previously mentioned significant competition between operators. In practice 

the transfer of used knowledge does not exist in the field of telecommunica-

tions data mining, because operators protect their experience. They treat the 

knowledge acquired, by using data mining methods, as a part of their com-

petitive advantage (Muraszkiewicz, 2000) 

 The study of the predictive potential, which is implemented in available 

commercial Decision Support Systems (e.g. PROPHIKS,
 
KOBAT-SAIR,

 

KOBAT-SAD), encourages one to conduct research into other approaches to 

forecasting of the demand for telephone services, and to assess their imple-

mentation techniques. Commercial software to conduct data mining calcula-

tion is not always effective in solving tasks, which are important for tele-

communications operators. It is ineffective particularly in solving problems 

where there are more complex data structures and temporal dependences, i.e. 

sequences of events (Muraszkiewicz, 2000). 

 The results of the conducted research, which has been described in this 

article, relate to one of the PS components, i.e. the internal characteristics 

forecasting techniques, namely sales expectations techniques. The purpose 

of this study is to verify the effectiveness of the constructed model in short-

term forecasting of the demand for telephone services. The linear regression 

model, including dichotomous (binary) explanatory variables, was integrated 

with the SARIMA model. This integration was based on the assumption that 

the regression model was supported by the SARIMA model. Thus the re-

gression model is used as a filter of modelled variability of demand for tele-

phone operator services (response variable). In turns the SARIMA model is 

used to reflect the remaining volatility of the demand for electronic commu-

nications services, i.e. received after the filtration of the origin variability of 

the modelled demand. 

 The author formulated the thesis, with regard to approximation and pre-

diction, supported linear regression model enables better results in compari-

son to non-supported linear regression model. Effectiveness comparison of 

the above mentioned two techniques (integrated and non-integrated model) 

was verified by means such obtained values as: fit coefficients, autocorrela-

tion coefficients, partial autocorrelation coefficients, and the average errors 

of expired forecasts ex-post. 

 The calculation study was carried out on the basis of data provided by 

one of the telecommunications network operators. The range of empirical 

material consisted of hourly counted seconds of outgoing calls within the 

framework of: given subscriber group, particular day (e.g. working or non-

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Paweł Kaczmarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 41–57 

44 

working), and specific category of connection (7 categories of connections 

were taken into account). 

2. The Theoretical Conception of the Prepared Model  

 The configuration of the forecasting model of demand for electronic 

connection services depends on the forecasting horizon. If the purpose of 

constructing the model is long-term prediction, apart from obvious quantita-

tive changes, qualitative changes should also be considered. Quantitative 

changes are based on changes in the value of the response variable according 

to the detected regularity, e.g. the regression function. On the other hand, 

qualitative changes are transformations of the essential features of the phe-

nomenon, such as the transformation of the existing regularity, which is ex-

pressed by the change of parameters or function type of the model (Nadolny, 

2011). 

 If the purpose of the modelling is short-term and medium-term predic-

tion, the qualitative changes mentioned above do not occur or occur in trace 

dimension. Therefore, it is not necessary to include them in the prognostic 

process. When a model is created for short and medium forecast horizon, the 

following factors should be considered: the type of day (typical working day, 

Saturday, Sunday, high days, and holidays) hour of the day, category of con-

nection, the type of subscribers, promotions (Kaczmarczyk, 2016). 

  The author applied the approach consisting of several segments. The 

approach is based on the fusion of the results obtained with the use of two 

different models, i.e. the linear multiple regression model and the SARIMA 

(p,d,q)(P,D,Q)s model. The first one is used to isolate the linear relationship 

between the dependent variable and independent variables, and the second 

one is used to model the residual values of the first model. This is shown in 

Figure 1.   

 In the first segment, the linear (multiple) regression model is estimated. 

The regression model enables one to obtain typical demand values for tele-

communications services that are generated by the specified subscriber 

group on the particular hours of the given type of day, within the particular  

category of connection. In the second segment, the residual values are calcu-

lated (i.e. cleaning time series of the response variable). The first and the 

second segments can only execute their tasks in the proposed sequence. The 

third segment serves to forecast the demand by using the regression model, 

and the fourth segment serves to forecast the residual values of the regres-

sion model. In the fourth segment the SARIMA model is used to model and 

forecast a lower variability (after elimination of the multiple relationships 



Microeconometric Analysis of Telecommunication Services Market… 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 41–57 

45 

included in regression model). The third and fourth segments can work col-

laterally. The results received by using the forecasting tools were integrated 

in the fifth segment, i.e. the forecast values obtained with the use of the re-

gression model are corrected by the prognostic residual values. The econo-

metric analysis of high frequency data was researched by Kufel (2010). 

Methods of elimination of deterministic components are a very important 

issue because they have a great impact on the accuracy of forecasts (Box et 

al., 1994; Makridakis and Wheelwright 1989; Makridakis et al., 1998). 

Figure 1. The integration of regression and SARIMA model 

3. The Research Results 

 In the conducted empirical analyses, the demand for telephone services 

(response variable) was considered as the hourly call time measurements 

(sec.) of outgoing connections of the telecommunications operator network. 

As the classification factors of the demand were assumed: hour within 24 

hours, type of 24 hours, connection category, and the kind of subscribers 

group. Within the framework of every mentioned classification factor were 

defined particular levels. Therefore the following 35 variables were defined: 

BUS – business subscribers, IND – individual subscribers, MN – mobile 

networks, LC – local calls to the same network, LCO – local calls to other 

networks, TC – trunk calls, IC – international calls, OC – other connections, 

2. Residuals calculation 

zt  = yt – ŷt    t = 1, ..., n 

1. Regression model   

estimation 

titi

m

i
t xaay ξ+Σ+=

1=
0

 

t = 1, ..., n 

 

3. Prediction of the 

dependent variable 

value 

)(
*

hnii

m

i
hn xaay +

1=
0+ Σ+=

 

5. Results aggregation 

and forecast accu-

racy assessment  

4. SARIMA model 

estimation and pre-

diction of the re-

sidual value ( *
htz +
) 

sQDPqdpARIMA ),,)(,,(  

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Paweł Kaczmarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 41–57 

46 

W – working 24 hours, SAT – Saturday, SUN – Sunday, and 24 variables to 

describe particular hours during the day: from 12AM – 00:00:00–01:00:00 to 

11PM – 23:00:00–00:00:00. 

 Hourly averages of the demand for telephone services in 24-hours cy-

cles, within the selected working 24 hours (Wednesdays) and generally non-

working 24 hours (Sundays) during a year and generated by business or in-

dividual subscribers, are presented in Figure 2.  

 

 

Figure 2. The average time (sec.) of outgoing calls generated by business or individ-

ual customers in hours of working and non-working 24 hours 

 The courses of the demand for telecommunications services are different 

due to the category of connection, subscriber group and type of 24 hours. 

The analytical sections have different location of the demand extreme.  

 The structure (categorised histogram) of demand values (hourly counted 

seconds of outgoing calls) generated by business customers, within working 

and non-working 24 hours, is shown in Figure 3. Figure 3 was drawn on the 

basis of the same statistical material that was used to present daily course of 

demand (generated by business customers) in Figure 2. Visual analysis leads 

to the remark that the variables distributions within the framework of busi-

ness subscribers are different, and the variable LCO has the highest observa-

Working 24 hours (business customers)  Sundays (business customers) 
 

Working 24 hours (individual customers)  Sundays (individual customers) 
 



Microeconometric Analysis of Telecommunication Services Market… 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 41–57 

47 

tions in the both types of days. The lowest values were observed in the case 

of the variable IC and OC. A relatively high value may be observed also 

within LC variable and may be noticed within working 24 hours as well as 

within Sundays.  

 
Working 24 hours 

 
Sundays 

Figure 3. The structure of observations (hourly counted sec.) of outgoing calls gen-

erated by business customers during working and non-working 24 hours 

 In the next figure (Figure 4), categorised histogram of hourly combined 

seconds of outgoing calls generated by individual subscribers also during 



Paweł Kaczmarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 41–57 

48 

working and non-working 24 hours is presented. It can be noticed in both 

types of day that the highest observations there are within the framework of 

local connection to other network and these observations are even higher 

than in the case business subscribers within this category and during the 

same type of day. The demand value within remaining categories of connec-

tion during both type of 24 hours are significantly lower. 

 
Working 24 hours 

 
Sundays 

Figure 4. The structure of observations (hourly counted sec.) of outgoing calls gen-

erated by individual customers during working and non-working 24 hours  



Microeconometric Analysis of Telecommunication Services Market… 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 41–57 

49 

 The intervals of hourly counted seconds of outgoing calls are left-open 

and right-closed. Therefore, the intervals (–50000, 0] or (–5000, 0] include 

the observations that equal to 0. This assumption enables isolation of the 

observations that equal to 0 and consequently it allows for better overview of 

the structure (categorised histogram) of the demand for telecommunication 

services generated by particular subscribers group, within defined type of 

day. In this analysis, the volumes of demand that equal to 0 constitute signif-

icant group of observations and these observations can be isolated in sepa-

rated interval. 

 The regression model has included 35 dichotomous independent vari-

ables, which were specified at the beginning of this study section. Independ-

ent variables take value 0 or 1. The dependent variable was set by hourly 

measurements of seconds of outgoings calls of the operator network. Multi-

ple regression parameters were estimated from data for the period from 1st 

January to 20th February of the selected year (14688 cases). The data, which 

was used to construct the tested models, was very complex. The constructed 

regression model was based on data relating to six categories of connections 

and two subscriber groups (12 separated analytical sections of demand). Due 

to the fact that the period from 1th January to 20th February consist of 1224 

hours, the modelling of full variability of demand for telecommunication 

connections services needed to involve 14688 cases. Therefore, the number 

of cases reflects joint analysis of demand in terms of various analytical sec-

tions at the same time.  

 Due to the fact that ridge regression was estimated, it was necessary to 

optimise parameter λ. The optimal value of the parameter λ was set at 

0.0570. At this value the ridge regression model was the best fitted to the 

modelled data (R
 
square = 0.4748; std. error of the estimate = 59524.1568; 

calculated F statistic = 378.4818 on 35 and 14,652 df, p < 0.05). In the ob-

tained regression model only one of the structural parameters, i.e. parameter 

standing by the variable 09PM, was statistical insignificant – see Table A1 in 

appendix.  

 Then the object of the research was autocorrelation function and the 

partial autocorrelation function of the regression model residuals. The re-

siduals of the regression model are characterised by transparent repetitions in 

24-hour cycles. The result of the autocorrelation analysis is presented in 

Figure 5. The regression model was constructed for almost full variability 

(many levels of applied classification factors) of demand for telecommunica-

tions connections services. The estimated model possibilities are too low to 

model such complex variability. This was the reason that autocorrelation was 

in the error term.  



Paweł Kaczmarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 41–57 

50 

 Forecasting procedure (by the use of regression and constructed inte-

grated model) was conducted with the use of the period from 21st to 28th of 

February (2304 forecasts). The predictive activity was conducted in all the 

assumed analytical section. Therefore the demand course was forecasted in 

section of: 24 hours, subscribers groups and connections categories. 

 
The autocorrelation function The partial autocorrelation function 

Figure 5. The autocorrelation function and the partial autocorrelation function of the 

regression model residuals 

 The demand forecasts accuracy was verified by using the mean absolute 

error (MAE) and the root mean square error (RMSE) according to the follow-

ing formulas:  

∑
1

*1 T

nt

tt yy
nT

MAE





   (1) 

∑
1

2* )(
1 T

nt

tt yy
nT

RMSE





  (2) 

where T  – forecast horizon, and n  – a number of observations, which were 

used to estimated model. 

 The research results, of the forecasting effectiveness of the regression 

model by the use of the above errors (in sec.), were 43148.92 and 57409.18 

for MAE and RMSE respectively. 

 The analysis of the regression residuals shows that they are characterised 

by seasonality in daily courses and in particular analytical section. In con-

nection with the seasonality, the thesis can be formulated that the use of the 

SARIMA model to reflect residuals variability allows for improving results 

in terms of approximation and forecasting of the analysed demand. More-

over, the analysis of the calculated Cook’s distances and the obtained stan-

dardised residuals indicate that there are unusual observations, i.e. influence 



Microeconometric Analysis of Telecommunication Services Market… 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 41–57 

51 

observations or outliers (see Figure A1 in appendix). Due to the risk of oblit-

eration of real patterns occurring in the studied phenomenon, the unusual 

observation were not eliminated and not replaced by their estimates 

(Dittmann et al., 2011). General overview of residuals course for business 

and then individual subscribers is presented in Figure 6.  

 

Figure 6. The regression residuals course 

 The data used to estimate the regression model included patterns from 

each analytical section of the demand, so the regression residuals course is 

different in particular intervals of observations. The highest residuals values 

can be observed in the interval of the local connection to other network gen-

erated by individual subscribers (the interval of observations 8089–8832 in 

January and the interval of observations 12289–12768 in February). The 

high values of residuals were also noticed in the interval of the local connec-

tion to other networks generated by business subscriber, but these observa-

tions were obviously lower than in the case of the individual subscribers. 

These results came from the highest values of the demand for telephone 

services within the framework of this category of connection in both groups 

of customers. The analysis of the regression residuals confirms the remarks 

on categorised histogram and interaction plot (Figure 1–3). 

 Several SARIMA models were tested. The maximum likelihood estima-

tion (MLE) was applied. Two approaches i.e. MLE according to Melard 

(1984), also known as exact likelihood, and MLE according to McLeod and 

Sales (1983) were used. The maximum likelihood estimation according to 

Salad and Macleod (1984) was also used. The criterion for assessing the 

model fit were squared errors of the SARIMA model. The initial sum of 

squared errors (ISS), final sum of squared errors (FSS) and mean of squared 

errors (MS) were taken into account. The goodness of fit was also assessed 

due to the percentage relation of these errors (RSS = FSS/ISS). In the all 

Business subscribers Individual subscribers 
 



Paweł Kaczmarczyk 

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52 

experiments the estimation process was stopped when the convergence crite-

rion (required accuracy) was reached. Thus, it was assumed that the changes 

in the SARIMA parameters over consecutive iterations should be less than 

the value of the convergence criterion. The optimal model was SARIMA 

(1,0,3)(1,0,4)24. The goodness of the best SARIMA model fit is presented in 

Table 1. 

Table 1. Summary of the SARIMA (1,0,3)(1,0,4)24 

Coefficient Value  

ISS 49.7153 
FSS 4.5122 
RSS 9.0761 
MS 0.0003 

Note: The value of ISS, FSS, and MS was presented in trillions and RSS in per cent. Convergence crite-

rion was set at 0.0001. The estimation process reached convergence criterion after cumulatively 46 itera-
tions. The parameters was obtained by the use of MLE according to McLeod and Sales (9 iterations) and 

then MLE according of Melard (37 iterations). 

All of the model parameters were statistically significant. The values and 

standard errors of the parameters were juxtaposed in Table 2.  

Table 2. Parameters and their errors of SARIMA (1,0,3)(1,0,4)24 

Coeff. 
 Non-seasonal parameters Seasonal parameters 

p(1) q(1) q(2) q(3) P(1) Q(1) Q(2) Q(3) Q(4) 

Parameter 0.75 –0.19 –0.19 –0.10 0.97 0.64 0.25 –0.03 –0.11 
ASE 0.01 0.01 0.01 0.01 0.00 0.01 0.01 0.01 0.01 
A t(14684) 82.99 –15.06 –17.11 –11.18 374.08 71.43 24.40 –2.67 –9.88 
LLC 0.73 –0.21 –0.21 –0.12 0.96 0.62 0.23 –0.05 –0.13 
ULC 0.77 –0.16 –0.17 –0.08 0.97 0.66 0.27 –0.01 –0.08 

Note: Non-seasonal parameters and also seasonal parameters are statistically significant at significance 
level p = 0,05. Explanation of the abbreviations: ASE – asymptotic standard error, A t(14684) – asymp-

totic t(14684), LLC – lower limit of confidence interval (95%), ULC – upper limit of confidence interval 
(95%). 

 The course of SARIMA (1,0,3)(1,0,4)24 residuals (for both subscribers 

groups) shows that their values are much lower than in the case of the re-

gression model and the variability reflecting of demand for telephone ser-

vices was improved (Figure 7). 

 Then the estimated value of the regression residuals (that were obtained 

by using the SARIMA model) were applied to correction estimated value of 

the demand (determined values of regression). The goodness of the fit to 

data for the final model, which was verified by means of R square, was 

0.9480. Therefore the level of fit was clearly higher in comparison to the 

regression, which was not supported by the SARMIA model.  



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53 

 

Figure 7. The residuals of SARIMA (1,0,3)(1,0,4)24 

 The analysis of obtained values of Q Box and Ljung coefficients and 

also partial correlation coefficients (Figure 8) indicate that they are much 

lower than the values of these coefficients, which were calculated in the 

analysis of regression model residuals (Figure 5). However they can be con-

sidered as not fully satisfactory. It is noticeable that there are still repetitions 

in 24 cycles (but smaller than previously). The results provide rationales to 

further research to reduce correlation in error term. The reduction of the 

correlation in terms of error could be probably achieved by reduction of such 

high numbers of the analytical section included in the regression model.  

 

Figure 8. The autocorrelation function and the partial autocorrelation function of the 

residuals of the supported regression  

Then the forecasting effectiveness of the supported regression model was 

verified and compared with the previous regression model. Average fore-

casting errors for the forecast period (the same as in the case of non-

Business subscribers Individual subscribers 
 

The autocorrelation function The partial autocorrelation function 



Paweł Kaczmarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 41–57 

54 

supported regression), accounted according to (1) and (2) formulas, amount 

to 8488.65 and 15758.65 respectively. These results can be objectively con-

sidered as much better than the result obtained by using the previous regres-

sion model, i.e. the forecasting effectiveness (in the mean of forecast accu-

racy) was significantly higher.  

Conclusions 

 In the light of the obtained research, the thesis can be confirmed that the 

supported regression model enables higher efficiency of approximation and 

prediction of demand for telecommunications services in comparison with 

the non-supported regression model. 

 The results encourage further research in the explored field. The fit and 

forecasts accuracy could probably be higher by the volatility reflecting 

within the framework of lower number of the analytical sections, for exam-

ple by the volatility modelling only within the business group, or even only 

within the business group and working 24-hours. The separation of particular 

types of day is especially important, because cycles of repetitions of daily 

demand during the same day in different categories of connection are similar 

in terms of the phases of the cycles. 

 It is also interesting to try to improve the fit of the constructed model by 

creating demand patterns in particular analytical sections, i.e. by using aver-

ages for the particular hours within the sections. This could contribute to 

a better fit of the regression model and consequently better fit of the overall 

model. In this approach one could also use separate information for separate 

models. 

 Further research could concern another realisation of the fourth segment. 

Thus future work may relate to the use of other modelling and forecasting 

methods for seasonality, i.e. the residuals of the regression model. 

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Mikroekonometryczna analiza rynku telekomunikacyjnego  
z wykorzystaniem modeli SARIMA 

Z a r y s  t r e ś c i. W artykule przedstawiono wyniki testów efektywności wieloprzekrojowe-

go modelu w krótkookresowym prognozowaniu cogodzinnego zapotrzebowania na usługi 

telefoniczne. Model został oparty na integracji zero-jedynkowego modelu regresji liniowej i 

modelu SARIMA. Model regresji spełnia rolę filtra modelowanej zmienności popytu na 

usługi telefoniczne. Model SARIMA służy do modelowania pozostałej zmienności. Badania 

wykazały, że proponowana integracja zapewnia wyższe możliwości aproksymacyjne i pre-

dykcyjne w porównaniu z niezintegrowanym modelem regresji liniowej. Wyniki badań sta-

nowią dla operatora wsparcie procesu planowania operacyjnego.  

S ł o w a  k l u c z o w e: System Wspomagania Decyzji, regresja zero-jedynkowa, model 

SARIMA, prognozowanie.  

 

 
 

http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.ekon-element-59348fa7-e43f-3ca4-90f1-cee018b3fb04
http://dx.doi.org/10.2307/2347672


Paweł Kaczmarczyk 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 41–57 

56 

Appendix  

Table A1.  The results of the multiple regression estimation 

Variable Standardised parameters and errors          Non-standardised parameters and errors  

β Std. error of β B Std. error of B T(14652) 

   39380.4034* 5205.2949 7.5655 
BUS –0.0354 0.01798 –5802.9220* 2949.3400 –1.9675 
IND 0.0354 0.01798 5802.9224* 2949.3400 1.9675 
MN –0.0975 0.01134 –21455.2156* 2495.9717 –8.5959 
LC 0.3342 0.01134 73567.5588* 2495.9717 29.4745 
LCO 0.1548 0.01134 34071.6527* 2495.9717 13.6507 
TC –0.0336 0.01134 –7389.2377* 2495.9717 –2.9605 
IC –0.1819 0.01134 –40032.2150* 2495.9717 –16.0387 
OC –0.1761 0.01134 –38762.5432* 2495.9717 –15.5300 
W –0.0962 0.00758 –39485.9177* 3110.7645 –12.6933 
SAT –0.1020 0.00758 –41857.1040* 3110.7645 –13.4556 
SUN –0.1032 0.00758 –42371.4863* 3110.7645 –13.6209 
12AM –0.1036 0.00758 –42524.3610* 3110.7645 –13.6701 
01AM –0.1038 0.00758 –42627.5665* 3110.7645 –13.7032 
02AM –0.1029 0.00758 –42233.6372* 3110.7645 –13.5766 
03AM –0.0936 0.00758 –38416.3277* 3110.7645 –12.3495 
04AM –0.0525 0.00758 –21547.7074* 3110.7645 –6.9268 
05AM 0.0348 0.00758 14268.2139* 3110.7645 4.5867 
06AM 0.1016 0.00758 41724.4466* 3110.7645 13.4129 
07AM 0.1204 0.00758 49438.9906* 3110.7645 15.8929 
08AM 0.1124 0.00758 46126.3489* 3110.7645 14.8280 
09AM 0.1043 0.00758 42806.7784* 3110.7645 13.7609 
10AM 0.1027 0.00758 42157.8503* 3110.7645 13.5522 
11AM 0.0852 0.00758 34987.4733* 3110.7645 11.2472 
12PM 0.0476 0.00758 19547.3911* 3110.7645 6.2838 
01PM 0.0299 0.00758 12294.3716* 3110.7645 3.9522 
02PM 0.0297 0.00758 12210.4834* 3110.7645 3.9252 
03PM 0.0486 0.00758 19952.9375* 3110.7645 6.4142 
04PM 0.0619 0.00758 25430.5249* 3110.7645 8.1750 
05PM 0.0327 0.00758 13441.3084* 3110.7645 4.3209 
06PM –0.0023 0.00758 –939.0656* 3110.7645 –0.3019 
07PM –0.0608 0.00758 –24963.2014* 3110.7645 –8.0248 
08PM –0.0912 0.00758 –37420.7441* 3110.7645 –12.0294 
09PM 0.0838 0.01712        14808.3710 3027.1566 4.8918 
10PM –0.0416 0.01325 –9923.5595* 3158.3647 –3.1420 
11PM –0.0644 0.01443 –13852.4642* 3105.0410 –4.4613 

Note:  * denote significance at 5% level.  

 

 

 



Microeconometric Analysis of Telecommunication Services Market… 

DYNAMIC ECONOMETRIC MODELS 17 (2017) 41–57 

57 

 

Figure A1. Normal probability plot of the regression residuals 

 

 

 

 

 


