Modelling Volatile Time Series with V-Transforms and Copulas

An approach to the modelling of volatile time series using a class of uniformity-preserving transforms for uniform random variables is proposed. V-transforms describe the relationship between quantiles of the stationary distribution of the time series and quantiles of the distribution of a predictable volatility proxy variable. They can be represented as copulas and permit the formulation and estimation of models that combine arbitrary marginal distributions with copula processes for the dynamics of the volatility proxy. The idea is illustrated using a Gaussian ARMA copula process and the resulting model is shown to replicate many of the stylized facts of financial return series and to facilitate the calculation of marginal and conditional characteristics of the model including quantile measures of risk. Estimation is carried out by adapting the exact maximum likelihood approach to the estimation of ARMA processes, and the model is shown to be competitive with standard GARCH in an empirical application to Bitcoin return data.

Maximum Likelihood Embedding of Logistic Random Dot Product Graphs

A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph visualizing and clustering. A latent space model of particular interest is the Random Dot Product Graph (RDPG), which can be fit using an efficient spectral method; however, this method is based on a heuristic that can fail, even in simple cases. Here, we consider a closely related latent space model, the Logistic RDPG, which uses a logistic link function to map from latent positions to edge likelihoods. Over this model, we show that asymptotically exact maximum likelihood inference of latent position vectors can be achieved using an efficient spectral method. Our method involves computing top eigenvectors of a normalized adjacency matrix and scaling eigenvectors using a regression step. The novel regression scaling step is an essential part of the proposed method. In simulations, we show that our proposed method is more accurate and more robust than common practices. We also show the effectiveness of our approach over standard real networks of the karate club and political blogs.

Estimation Parameter d in Autoregressive Fractionally Integrated Moving Average Model in Predicting Wind Speed

Wind speed is one of the most important weather factors in the landing and takeoff process of airplane because it can affect the airplane's lift. Therefore, we need a model to predict the wind speed in an area. In this research, the wind speed forecast using the ARIMA model is discussed which has differencing parameters in the form of fractions. This model is called the ARFIMA model. In estimating differencing parameters two methods are considered, namely parametric and semiparametric methods. Exact Maximum Likelihood (EML) is used under parametric method. Meanwhile, four methods semiparametric estmation are used, i.e Geweke and Porter-Hudak (GPH), Smooth GPH (Sperio), Local Whittle and Rescale Range (R/S). The result shows the best estimation method is GPH with the selected model is ARFIMA (2,0.334,0).Keywords: ARFIMA, Parametric Method, Semiparametric Method. AbstrakKecepatan angin merupakan salah satu faktor cuaca yang penting dalam proses pendaratan dan tinggal landas pesawat karena dapat mempengaruhi daya angkat pesawat. Oleh karena itu, diperlukan suatu model untuk memprakirakan kecepatan angin di suatu wilayah. Artikel ini membahas prakiraan kecepatan angin dengan menggunakan model ARIMA yang memiliki parameter differencing berupa bilangan pecahan. Model ini disebut model ARFIMA. Pada estimasi parameter differencing terdapat dua metode yang digunakan pada penelitian ini, yaitu metode parametrik dan metode semiparametrik. Metode parametrik yang digunakan adalah Exact Maximum Likelihood (EML) dan empat metode semiparametrik yang digunakan adalah Geweke and Porter-Hudak (GPH), Smooth GPH (Sperio), Local Whittle dan Rescale Range (R/S). Hasil analisis menunjukkan pada kasus ini metode estimasi terbaik adalah GPH dengan model terpilih adalah ARFIMA(2,0.334,0).Kata kunci: ARFIMA, Metode Parametrik, Metode Semiparametrik.

On Local Linear Approximations to Diffusion Processes

Diffusion models have been used extensively in many applications. These models, such as those used in the financial engineering, usually contain unknown parameters which we wish to determine. One way is to use the maximum likelihood method with discrete samplings to devise statistics for unknown parameters. In general, the maximum likelihood functions for diffusion models are not available, hence it is difficult to derive the exact maximum likelihood estimator (MLE). There are many different approaches proposed by various authors over the past years, see, for example, the excellent books and Kutoyants (2004), Liptser and Shiryayev (1977), Kushner and Dupuis (2002), and Prakasa Rao (1999), and also the recent works by Aït-Sahalia (1999), (2004), (2002), and so forth. Shoji and Ozaki (1998; see also Shoji and Ozaki (1995) and Shoji and Ozaki (1997)) proposed a simple local linear approximation. In this paper, among other things, we show that Shoji's local linear Gaussian approximation indeed yields a good MLE.

Thrombotic complications in adult patients with lymphoma: a meta-analysis of 29 independent cohorts including 18 018 patients and 1149 events

Thrombotic complications in hematologic malignancies have important clinical implications. In this meta-analysis we sought to obtain accurate estimates of the thrombotic risk in lymphoma patients. Articles were searched in electronic databases and references. Eighteen articles were identified (29 cohorts, 18 018 patients and 1149 events). Pooled incidence rates (IRs) were calculated by the use of a method based on the exact maximum likelihood binomial distribution. The global IR of thrombosis was 6.4% (95% confidence interval [CI] 6.0%-6.8%). The global IRs of venous or arterial events were 5.3% (95% CI, 5.0%-5.7%) and 1.1% (95% CI, 0.9%-1.2%), respectively. The IR of thrombosis observed in subjects with non-Hodgkin lymphoma (NHL) was 6.5% (95% CI, 6.1%-6.9%), significantly greater than that observed for patients with Hodgkin lymphoma (4.7%; 95% CI, 3.9%-5.6%). Within NHL, patients with high-grade disease had a greater risk of events (IR 8.3%; 95% CI, 7.0%-9.9%) than low-grade disease (IR 6.3%; 95% CI, 4.5%-8.9%). This meta-analysis shows that the IR of thrombosis in lymphoma patients is quite high, especially in those with NHL at an advanced stage of the disease. These results may help better defining lymphoma populations at high thrombotic risk, to whom prophylactic approaches could be preferentially applied.