Seasonally and Fractionally Differenced Time Series

fractional differencing, Lagrange multiplier test, long memory, seasonal differencing, seasonal persistence

Asymptotic Prediction Mean Squared Error for Strongly Dependent Processes with Estimated Parameters

In this paper we deal with the prediction theory of long memory processes. After investigating the general theory relating to convergence of moments of the nonlinear least squares estimators, we evaluate the asymptotic prediction mean squared error of two predictors. One is defined by using the estimator of the differencing parameter and the other is defined by using a fixed, known differencing parameter, which is, in other words, one parametric predictor of the seasonally integrated autoregressive moving average (SARIMA) models. In this paper, results do not impose the normality assumption and deal not only with stationary time series but also with nonstationary ones. The finite sample behavior is examined by simulations using the computer program S-PLUS in terms of the asymptotic theory.Mean-squared prediction errosrs, Long memory, Seasonality, Nonlinear least squares estimators, Convergence of moments

Seasonally and Fractionally Differenced Time Series (revised, August 2006)

This paper deals with a generalized seasonally integrated autoregressive moving average (SARIMA) model, which allows the two differencing parameters to take on fractional values. After investigating the basic properties of the model, we examine the asymptotic properties of the estimators and statistics without assuming normality. It is shown that the standard asymptotic results hold for the tests and the estimators; that is, the conditional sum of squares estimator is strongly consistent and tends towards normality, the Lagrange multiplier (LM) test and the Wald test statistics are more powerful than the old Portmanteau test statistics, and Godfrey's LM test is also applicable. The finite behaviour of the tests and estimators is also examined by simulations, and the source of differences in behaviour is made clear in terms of the asymptotic theory.Fractional differencing, Lagrange multiplier test, Long memory, Seasonal differencing, Seasonal persistence

Chi-Squared Portmanteau Statistics for Vector Autoregressive Models with Uncorrelated Errors

The portmanteau statistic based on the first m residual autocorrelations is used for testing the goodness-of-fit for vector autoregressive models with varying m. However, it is known that existing portmanteau statistics are approximately non chi-squared distributions in the presence of non-independent innovations. In this paper we propose a new portmanteau statistic that is asymptotically chi-squared even in the presence of non-independent innovations. We also study the joint probability of the multiple portmanteau statistics with different degrees of freedom. Monte Carlo experiments illustrate the finite sample performance for the proposed portmanteau test

合理的バブルの検定の検出力について

国内株価指数(TOPIX)において1990年前後に合理的バブルが生起していたかどうかの検定を行う.この検定は自己回帰（Auto-regressive, AR）モデルによる単位根検定に帰着される．ただし対立仮説は定常AR(1)モデルによる左片側定ではなくexplosive AR(1)モデルによる右片側検定である．この右片側検定ならびにモデルに構造変化を加味した検定は未整備である．そのため，この検定における主要な検定統計量であるAugumented Dickey-Fuller(ADF)検定統計量とその改良型(recursive，rolling)の検出力を理論とシミュレーションの両面から検証した．これら検定統計量は，TOPIXの合理的バブルを検出した．検出された期間は1986年から1990年にかけてで景気循環との整合性も確認された

コンビニレジの混雑の要因とコロナ禍・レジ袋有料化・電子決済の影響の分析

コンビニレジの混雑の問題解決のため、2019年11月と2020年12月の2回にわたり、ファミリーマート関大店（以下FMKと略）でレジの決済の観察調査を行った。これら2回の調査期間をまたぎ、コロナ禍・レジ袋有料化・電子決済の普及による影響を受けた。グラフと記述統計の分析より、消費者のレジの決済時の特徴とレジの決済時間の関係にも変化が観察され、次がわかった。1.　消費者のできる混雑緩和（レジの決済時間の短縮）には、レジ袋を辞退する、事前に決済の準備をする、ポイントと決済はスマホで行い、レシートを受け取らないのが有効と推察される（2020年12月の調査時点、3.3節、4.1節、4.11節）。これら行動を全てとった場合、平均約4割程度のレジの決済時間の短縮につながることが分かった。またこれら行動は、プラスチックごみの削減や、新型コロナウイルスの感染防止策としても有効であろう。2.　レジの決済時間の分布から、2019年調査と比較して、2020年の調査は、非常に長時間、レジの決済をする層が減り、短時間ですます層が増えた（3.1節）。しかしながら、レジ決済時間の平均は、2019年と2020年では、さほど大きな差は見られなかった（3.1節）。3.　電子決済の普及による影響は、2019年と2020年の比較をして、明らかな比率の変化が見られなかった（3.2節）。しかしながら、コロナ禍の影響も考えられるが、消費者は電子決済と現金決済、いずれか一方のみを選択する傾向が顕著となった（3.3節）。また、電子決済がレジの決済時間の短縮につながることが示された（4.1節、4.11節）。4.　コロナ禍による影響と思われる現象として、品数を一度に多く買う客層の比率の増加、決済の準備をする消費者の比率の増加、おつり・レシートの辞退率の増加が観察された（3.2節）。5.　レジ袋有料化の影響として、レジ袋辞退率が有料化前と比べて、22％から76％と大きく変化した。これはファミリーマートのプレスリリースや環境省の調査より、FMKではより有料化の効果が表れたことを示している（3.2節）。また、2020年調査より、レジ袋辞退は、レジの決済時間の時短にもつながる傾向があることが分かった（3.3節、4.1節、4.11節）

Dependence of Photocatalytic Activity on Aspect Ratio of Shape-Controlled Rutile Titanium(IV) Oxide Nanorods

Shape-controlled rutile titanium(IV) oxide (TiO2) nanorods with various aspect ratios were prepared by two-step synthesis in the presence of two kinds of inorganic anions. The first synthesis step from titanium(III) chloride solution induced the formation of aggregated needlelike rutile TiO2, the shape of which largely depended on the inorganic anion used. Moreover, shape-controlled rutile TiO2 rods with {110} side crystal faces and {111} and/or {001} edge crystal faces were obtained by hydrothermal treatment of the needlelike rutile TiO2. Their aspect ratios were largely influenced by the starting material used in the hydrothermal treatment. The photocatalytic activity for decomposition of acetaldehyde increased with decreasing aspect ratio because the surface area ratio of {111} and/or {001} to {110} exposed crystal faces, which are attributed to oxidation and reduction sites respectively, became more optimal

Femtosecond X-ray emission study of the spin cross-over dynamics in haem proteins

In haemoglobin (consisting of four globular myoglobin-like subunits), the change from the low-spin (LS) hexacoordinated haem to the high spin (HS) pentacoordinated domed form upon ligand detachment and the reverse process upon ligand binding, represent the transition states that ultimately drive the respiratory function. Visible-ultraviolet light has long been used to mimic the ligand release from the haem by photodissociation, while its recombination was monitored using time-resolved infrared to ultraviolet spectroscopic tools. However, these are neither element- nor spin-sensitive. Here we investigate the transition state in the case of Myoglobin-NO (MbNO) using femtosecond Fe Kalpha and Kbeta non-resonant X-ray emission spectroscopy (XES) at an X-ray free-electron laser upon photolysis of the Fe-NO bond. We find that the photoinduced change from the LS (S = 1/2) MbNO to the HS (S = 2) deoxy-myoglobin (deoxyMb) haem occurs in ca. 800 fs, and that it proceeds via an intermediate (S = 1) spin state. The XES observables also show that upon NO recombination to deoxyMb, the return to the planar MbNO ground state is an electronic relaxation from HS to LS taking place in ca. 30 ps. Thus, the entire ligand dissociation-recombination cycle in MbNO is a spin cross-over followed by a reverse spin cross-over process

Femtosecond time-resolved X-ray absorption spectroscopy of anatase TiO2 nanoparticles using XFEL

光触媒ナノ粒子における光照射後10兆分の1秒での電子の動きをX線自由電子レーザーで観測. 京都大学プレスリリース. 2017-07-06.The charge-carrier dynamics of anatase TiO2 nanoparticles in an aqueous solution were studied by femtosecond time-resolved X-ray absorption spectroscopy using an X-ray free electron laser in combination with a synchronized ultraviolet femtosecond laser (268 nm). Using an arrival time monitor for the X-ray pulses, we obtained a temporal resolution of 170 fs. The transient X-ray absorption spectra revealed an ultrafast Ti K-edge shift and a subsequent growth of a pre-edge structure. The edge shift occurred in ca. 100 fs and is ascribed to reduction of Ti by localization of generated conduction band electrons into shallow traps of self-trapped polarons or deep traps at penta-coordinate Ti sites. Growth of the pre-edge feature and reduction of the above-edge peak intensity occur with similar time constants of 300–400 fs, which we assign to the structural distortion dynamics near the surface

Thermodynamic instability of siRNA duplex is a prerequisite for dependable prediction of siRNA activities

We developed a simple algorithm, i-Score (inhibitory-Score), to predict active siRNAs by applying a linear regression model to 2431 siRNAs. Our algorithm is exclusively comprised of nucleotide (nt) preferences at each position, and no other parameters are taken into account. Using a validation dataset comprised of 419 siRNAs, we found that the prediction accuracy of i-Score is as good as those of s-Biopredsi, ThermoComposition21 and DSIR, which employ a neural network model or more parameters in a linear regression model. Reynolds and Katoh also predict active siRNAs efficiently, but the numbers of siRNAs predicted to be active are less than one-eighth of that of i-Score. We additionally found that exclusion of thermostable siRNAs, whose whole stacking energy (ΔG) is less than −34.6 kcal/mol, improves the prediction accuracy in i-Score, s-Biopredsi, ThermoComposition21 and DSIR. We also developed a universal target vector, pSELL, with which we can assay an siRNA activity of any sequence in either the sense or antisense direction. We assayed 86 siRNAs in HEK293 cells using pSELL, and validated applicability of i-Score and the whole ΔG value in designing siRNAs