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Modelling and forecasting student enrolment with Box -Jenkins and Holty-Winters methodologies : a case of North West University, Mafikeng Campous / David Selokela SebolaiSebolai, David Selokela January 2010 (has links)
Thesis (M.Statistics) North-West University, Mafikeng Campus, 2010
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Modelling of nonlinear dynamic systems : using surrogate data methodsConradie, Tanja 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2000. / ENGLISH ABSTRACT: This study examined nonlinear modelling techniques as applied to dynamic systems, paying
specific attention to the Method of Surrogate Data and its possibilities. Within the field of
nonlinear modelling, we examined the following areas of study: attractor reconstruction, general
model building techniques, cost functions, description length, and a specific modelling
methodology. The Method of Surrogate Data was initially applied in a more conventional
application, i.e. testing a time series for nonlinear, dynamic structure. Thereafter, it was used in a
less conventional application; i.e. testing the residual vectors of a nonlinear model for
membership of identically and independently distributed (i.i.d) noise.
The importance of the initial surrogate analysis of a time series (determining whether the apparent
structure of the time series is due to nonlinear, possibly chaotic behaviour) was illustrated. This
study confrrmed that omitting this crucial step could lead to a flawed conclusion.
If evidence of nonlinear structure in the time series was identified, a radial basis model was
constructed, using sophisticated software based on a specific modelling methodology. The model
is an iterative algorithm using minimum description length as the stop criterion. The residual
vectors of the models generated by the algorithm, were tested for membership of the dynamic
class described as i.i.d noise. The results of this surrogate analysis illustrated that, as the model
captures more of the underlying dynamics of the system (description length decreases), the
residual vector resembles Li.d noise. It also verified that the minimum description length
criterion leads to models that capture the underlying dynamics of the time series, with the residual
vector resembling Li.d noise. In the case of the "worst" model (largest description length), the
residual vector could be distinguished from Li.d noise, confirming that it is not the "best" model.
The residual vector of the "best" model (smallest description length), resembled Li.d noise,
confirming that the minimum description length criterion selects a model that captures the
underlying dynamics of the time series.
These applications were illustrated through analysis and modelling of three time series: a time
series generated by the Lorenz equations, a time series generated by electroencephalograhpic
signal (EEG), and a series representing the percentage change in the daily closing price of the
S&P500 index. / AFRIKAANSE OPSOMMING: In hierdie studie ondersoek ons nie-lineere modelleringstegnieke soos toegepas op dinamiese
sisteme. Spesifieke aandag word geskenk aan die Metode van Surrogaat Data en die
moontlikhede van hierdie metode. Binne die veld van nie-lineere modellering het ons die
volgende terreine ondersoek: attraktor rekonstruksie, algemene modelleringstegnieke,
kostefunksies, beskrywingslengte, en 'n spesifieke modelleringsalgoritme. Die Metode and
Surrogaat Data is eerstens vir 'n meer algemene toepassing gebruik wat die gekose tydsreeks vir
aanduidings van nie-lineere, dimanise struktuur toets. Tweedens, is dit vir 'n minder algemene
toepassing gebruik wat die residuvektore van 'n nie-lineere model toets vir lidmaatskap van
identiese en onafhanlike verspreide geraas.
Die studie illustreer die noodsaaklikheid van die aanvanklike surrogaat analise van 'n tydsreeks,
wat bepaal of die struktuur van die tydsreeks toegeskryf kan word aan nie-lineere, dalk chaotiese
gedrag. Ons bevesting dat die weglating van hierdie analise tot foutiewelike resultate kan lei.
Indien bewyse van nie-lineere gedrag in die tydsreeks gevind is, is 'n model van radiale
basisfunksies gebou, deur gebruik te maak van gesofistikeerde programmatuur gebaseer op 'n
spesifieke modelleringsmetodologie. Dit is 'n iteratiewe algoritme wat minimum
beskrywingslengte as die termineringsmaatstaf gebruik. Die model se residuvektore is getoets vir
lidmaatskap van die dinamiese klas wat as identiese en onafhanlike verspreide geraas bekend
staan. Die studie verifieer dat die minimum beskrywingslengte as termineringsmaatstaf weI
aanleiding tot modelle wat die onderliggende dinamika van die tydsreeks vasvang, met die
ooreenstemmende residuvektor wat nie onderskei kan word van indentiese en onafhanklike
verspreide geraas nie. In die geval van die "swakste" model (grootse beskrywingslengte), het die
surrogaat analise gefaal omrede die residuvektor van indentiese en onafhanklike verspreide
geraas onderskei kon word. Die residuvektor van die "beste" model (kleinste
beskrywingslengte), kon nie van indentiese en onafhanklike verspreide geraas onderskei word nie
en bevestig ons aanname.
Hierdie toepassings is aan die hand van drie tydsreekse geillustreer: 'n tydsreeks wat deur die
Lorenz vergelykings gegenereer is, 'n tydsreeks wat 'n elektroenkefalogram voorstel en derdens,
'n tydsreeks wat die persentasie verandering van die S&P500 indeks se daaglikse sluitingsprys
voorstel.
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Statistical forecasting and product portfolio managementNorvell, Joakim January 2016 (has links)
For a company to stay profitable and be competitive, the customer satisfaction must be very high. This means that the company must provide the right item at the right place at the right time, or the customer may bring its business to the competitor. But these factors bring uncertainty for the company in the supply chain of when, what and how much of the item to produce and distribute. For reducing this uncertainty and for making better plans for future demand, some sort of forecasting method must be provided. A forecast can however be statistically based and also completed with a judgmental knowledge if the statistics are not sufficient. This thesis has been done in cooperation with the Sales and Operations (S&OP) department at Sandvik Mining Rock Tools in Sandviken, where a statistical forecast is currently used in combination with manual changes from sales. The forecasts are used as base for planning inventory levels and making production plans and are created by looking at the history of sales. This is done in order to meet market expectations and continuously be in sync with market fluctuations. The purpose with this thesis has been to study the item- customer combination demand and the statistical forecasting process that is currently used at the S&OP department. One problem when creating forecast is how to forecast irregular demand accurately. This thesis has therefore been examining the history of sales too see in what extent irregular demand exists and how it can be treated. The result is a basic tool for mapping customers' demand behavior, where the behavior is decomposed into average monthly demand and volatility. Another result is that history of sales can get decomposed into Volatility, Volume, Value, Number of sales and Sales interval for better analysis. These variables can also be considered whenever analyzing and forecasting irregular demand. A third result is a classification of time series working as a guideline if demand should be statistically or judgmentally forecasted or being event based. The study analyzed 36 months history of sales for 56 850 time series of item- customer specific demand. The findings were that customers should have at least one year of continuous sales before the demand can be entirely statistically forecasted. The limits for demand to even be forecasted, the history of sales should at least occur every third month in average and contain at least six sales. Then the demand is defined as irregular and the forecast method is set to judgmental forecasting, which can be forecasted using statistical methods with manual adjustments. The results showed that the class of irregular demand represents approximately 70 percent in the aspect of revenue and therefore requires attention. / För att ett företag ska kunna vara lönsamt och konkurrenskraftigt måste kundnöjdheten vara mycket hög. Detta betyder att ett företag måste kunna förse rätt produkt i rätt tid på rätt plats, annars kommer kunden troligtvis att vända sig till konkurrenten. Men dessa faktorer kommer med osäkerhet för företaget i försörjningskedjan i när, vad och hur mycket av produkten de ska producera och distribuera. För att minska osäkerheten och för att planera bättre för framtida efterfrågan, måste någon typ av prognos upprättas. En prognos kan vara baserad på statistiska metoder men också kompletterad med subjektiv marknadsinformation om statistiken inte är tillräcklig. Studien som denna rapport beskriver är gjord i samarbete med Sales och Operations- avdelning (S&OP) på Sandvik Mining Rock Tools i Sandviken. Där används statistiska prognoser i kombination med manuella förändringar av säljare samt regionala planerare som bas för planering av lagernivåer och produktion. Detta gör man för att möta marknadens efterfråga och för att kontinuerligt vara uppdaterad med marknadens variationer. Syftet med detta arbete har varit att studera kunders efterfrågan av produkt- kund kombination och den metod som används vid statistiska prognoser hos S&OP- avdelningen. Ett problem som finns när man vill skapa prognoser är hur man ska prognostisera oregelbunden försäljning korrekt. Detta arbete har därför analyserat historisk försäljning för att se i vilken utsträckning oregelbunden efterfrågan finns och hur den kan hanteras. Resultatet är ett enkelt verktyg för att kunna kartlägga kunders köpbeteende. Ett till resultat är att historisk försäljning kan bli uppdelat i Volatilitet, Volym, Värde, Antalet köptillfällen och Tidsintervallet mellan köptillfällena. Dessa variabler kan även tas till hänsyn när man analyserar och prognostiserar oregelbunden försäljning. Ett tredje resultat är en klassificering av tidsserier som kan fungera som riktmärken om efterfrågan ska vara statistisk eller manuellt prognostiserade eller inte bör ha en prognos över huvud taget. Denna studie analyserade 36 månaders historik för 56 850 tidsserier av försäljning per produkt- kund kombination. Resultaten var att en kund bör ha åtminstone ett år av kontinuerlig efterfrågan innan man kan ha en prognos med statistiska modeller. Gränsen för att ens ha en prognos är att efterfrågan bör återkomma var tredje månad i genomsnitt och ha en historik av åtminstone sex försäljningstillfällen. Då klassificeras efterfrågan som oregelbunden och prognosen kan vara baserad på statistiska metoder men med manuella ändringar. I resultatet framkom det att oregelbunden efterfrågan representerar cirka 70 procent i avseende på intäkter och kräver således mycket uppmärksamhet.
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Time series forecasting and model selection in singular spectrum analysisDe Klerk, Jacques 11 1900 (has links)
Dissertation (PhD)--University of Stellenbosch, 2002 / ENGLISH ABSTRACT: Singular spectrum analysis (SSA) originated in the field of Physics. The technique is
non-parametric by nature and inter alia finds application in atmospheric sciences,
signal processing and recently in financial markets. The technique can handle a very
broad class of time series that can contain combinations of complex periodicities,
polynomial or exponential trend. Forecasting techniques are reviewed in this study,
and a new coordinate free joint-horizon k-period-ahead forecasting formulation is
derived. The study also considers model selection in SSA, from which it become
apparent that forward validation results in more stable model selection.
The roots of SSA are outlined and distributional assumptions of signal senes are
considered ab initio. Pitfalls that arise in the multivariate statistical theory are
identified.
Different approaches of recurrent one-period-ahead forecasting are then reviewed.
The forecasting approaches are all supplied in algorithmic form to ensure effortless
adaptation to computer programs. Theoretical considerations, underlying the
forecasting algorithms, are also considered. A new coordinate free joint-horizon kperiod-
ahead forecasting formulation is derived and also adapted for the multichannel
SSA case.
Different model selection techniques are then considered. The use of scree-diagrams,
phase space portraits, percentage variation explained by eigenvectors, cross and
forward validation are considered in detail. The non-parametric nature of SSA
essentially results in the use of non-parametric model selection techniques.
Finally, the study also considers a commercial software package that is available and
compares it with Fortran code, which was developed as part of the study. / AFRIKAANSE OPSOMMING: Singulier spektraalanalise (SSA) het sy oorsprong in die Fisika. Die tegniek is nieparametries
van aard en vind toepassing in velde soos atmosferiese wetenskappe,
seinprossesering en onlangs in finansiële markte. Die tegniek kan 'n wye
verskeidenheid tydreekse hanteer wat kombinasies van komplekse periodisiteite,
polinomiese- en eksponensiële tendense insluit. Vooruitskattingstegnieke word ook in
hierdie studie beskou, en 'n nuwe koërdinaatvrye gesamentlike horison k-periodevooruitskattingformulering
word afgelei. Die studie beskou ook model seleksie in
SSA, waaruit duidelik blyk dat voorwaartse validasie meer stabiele model seleksie tot
gevolg het.
Die agtergrond van SSA word ab initio geskets en verdelingsaannames van seinreekse
beskou. Probleemgevalle wat voorkom in die meervoudige statistiese teorie word
duidelik geïdentifiseer.
Verskeie tegnieke van herhalende toepassing van een-periode-vooruitskatting word
daarna beskou. Die benaderings tot vooruitskatting word in algororitmiese formaat
verskaf wat die aanpassing na rekenaarprogrammering vergemaklik. Teoretiese
vraagstukke, onderliggend aan die vooruitskattings-algortimes, word ook beskou. 'n
Nuwe koërdinaatvrye gesamentlike horison k-periode-vooruitskattingsformulering
word afgelei en aangepas vir die multikanaal SSA geval.
Verskillende model seleksie tegnieke is ook beskou. Die gebruik van "scree"-
diagramme, fase ruimte diagramme, persentasie variasie verklaar deur eievektore,
kruis- en voorwaartse validasie word ook aangespreek. Die nie-parametriese aard van
SSA noop die gebruik van nie-parametriese model seleksie tegnieke.
Die studie vergelyk laastens 'n kommersiële sagtewarepakket met die Fortran
bronkode wat as deel van hierdie studie ontwikkel is.
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Stochastic and chaotic behaviour of some hydrological time series賴飛丹, Lai, Feizhou. January 1992 (has links)
published_or_final_version / Civil and Structural Engineering / Doctoral / Doctor of Philosophy
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Analysis and prediction of hydrometeorological time series by dynamical system approachGurung, Ai Bahadur. January 2000 (has links)
published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy
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Topics in financial time series analysis: theory and applications方柏榮, Fong, Pak-wing. January 2001 (has links)
published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy
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Time series regression modelling of air quality data in Hong KongYan, Ka-lok., 忻嘉樂. January 1994 (has links)
published_or_final_version / Environmental Management / Master / Master of Science in Environmental Management
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Statistical inference of some financial time series modelsKwok, Sai-man, Simon., 郭世民. January 2006 (has links)
published_or_final_version / abstract / Statistics and Actuarial Science / Master / Master of Philosophy
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Assessing the effects of societal injury control interventionsBonander, Carl January 2016 (has links)
Injuries have emerged as one of the biggest public health issues of the 21th century. Yet, the causal effects of injury control strategies are often questioned due to a lack of randomized experiments. In this thesis, a set of quasi-experimental methods are applied and discussed in the light of causal inference theory and the type of data commonly available in injury surveillance systems. I begin by defining the interrupted time series design as a special case of the regression-discontinuity design, and the method is applied to two empirical cases. The first is a ban on the sale and production of non-reduced ignition propensity (RIP) cigarettes, and the second is a tightening of the licensing rules for mopeds. A two-way fixed effects model is then applied to a case with time-varying starting dates, attempting to identify the causal effects of municipality-provided home help services for the elderly. Lastly, the effect of the Swedish bicycle helmet law is evaluated using the comparative interrupted time series and synthetic control methods. The results from the empirical studies suggest that the stricter licensing rules and the bicycle helmet law were effective in reducing injury rates, while the home help services and RIP cigarette interventions have had limited or no impact on safety as measured by fatalities and hospital admissions. I conclude that identification of the impact of injury control interventions is possible using low cost means. However, the ability to infer causality varies greatly by empirical case and method, which highlights the important role of causal inference theory in applied intervention research. While existing methods can be used with data from injury surveillance systems, additional improvements and development of new estimators specifically tailored for injury data will likely further enhance the ability to draw causal conclusions in natural settings. Implications for future research and recommendations for practice are also discussed. / Injuries have emerged as one of the biggest public health issues of the 21th century. Yet, the causal effects of injury control strategies are rarely known due to a lack of randomized experiments. In this thesis, a set of quasi-experimental methods are discussed in the light of causal inference theory and the type of data commonly available in injury surveillance systems. I begin by defining the identifying assumptions of the interrupted time series design as a special case of the regression-discontinuity design, and the method is applied to two empirical cases. The first is a ban on the sale and production of non-fire safe cigarettes and the second is a tightening of the licensing rules for mopeds. A fixed effects panel regression analysis is then applied to a case with time-varying starting dates, attempting to identify the causal effects of municipality-provided home help services for the elderly. Lastly, the causal effect of the Swedish bicycle helmet law is evaluated using a comparative interrupted time series design and a synthetic control design. I conclude that credible identification of the impact of injury control interventions is possible using simple and cost-effective means. Implications for future research and recommendations for practice are discussed.
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