Autocorrelation Function Analysis Research Articles

Photon correlations in the collective emission of hybrid gold-(CdSe/CdS/CdZnS) nanocrystal supraparticles

We investigate the photon statistics of the light emitted by single self-assembled hybrid gold-CdSe/CdS/CdZnS colloidal nanocrystal supraparticles through the detailed analysis of the intensity autocorrelation function g (2)(τ). We first reveal that, despite the large number of nanocrystals involved in the supraparticle emission, antibunching can be observed. We then present a model based on non-coherent Förster energy transfer and Auger recombination that well captures photon antibunching. Finally, we demonstrate that some supraparticles exhibit a bunching effect at short time scales corresponding to coherent collective emission.

Investigating thermal conductivity and mechanical properties of a hybrid material based on cellulose nanofibers and boron nitride nanotubes using molecular dynamics simulations

Cellulose nanofibers (NFCs) have emerged as a preferred choice for fabricating nanomaterials with exceptional mechanical properties. At the same time, boron nitride nanotubes (BNNTs) have long been favored in thermal management devices due to their superior thermal conductivity (k). This study uses reverse non-equilibrium molecular dynamics (MD) simulations to investigate k for a hybrid material based on NFCs and BNNTs. The result is then compared with pure NFC and BNNT-based structures with equivalent total weight content to elucidate how incorporating BNNT fillers enhances k for the hybrid system. Furthermore, the fundamental phonon vibration modes responsible for driving thermal transport in NFC-based materials upon incorporating BNNTS are identified by computing the vibrational density of states from the Fourier transform analysis of the averaged mass-weighted velocity autocorrelation function. Additionally, MD simulations demonstrate how both NFCs and BNNTs synergistically improve the constituting hybrid structure’s mechanical properties (e.g. tensile strength and stiffness). The overarching aim is to contribute towards the engineered design of novel functional materials based on nanocellulose that simultaneously improve crucial physical properties pertaining to thermal transport and mechanics.

Quantification of blood flow index in diffuse correlation spectroscopy using a robust deep learning method.

Diffuse correlation spectroscopy (DCS) is a powerful, noninvasive optical technique for measuring blood flow. Traditionally the blood flow index (BFi) is derived through nonlinear least-square fitting the measured intensity autocorrelation function (ACF). However, the fitting process is computationally intensive, susceptible to measurement noise, and easily influenced by optical properties (absorption coefficient and reduced scattering coefficient ) and scalp and skull thicknesses. We aim to develop a data-driven method that enables rapid and robust analysis of multiple-scattered light's temporal ACFs. Moreover, the proposed method can be applied to a range of source-detector distances instead of being limited to a specific source-detector distance. We present a deep learning architecture with one-dimensional convolution neural networks, called DCS neural network (DCS-NET), for BFi and coherent factor () estimation. This DCS-NET was performed using simulated DCS data based on a three-layer brain model. We quantified the impact from physiologically relevant optical property variations, layer thicknesses, realistic noise levels, and multiple source-detector distances (5, 10, 15, 20, 25, and 30mm) on BFi and estimations among DCS-NET, semi-infinite, and three-layer fitting models. DCS-NET shows a much faster analysis speed, around 17,000-fold and 32-fold faster than the traditional three-layer and semi-infinite models, respectively. It offers higher intrinsic sensitivity to deep tissues compared with fitting methods. DCS-NET shows excellent anti-noise features and is less sensitive to variations of and at a source-detector separation of 30mm. Also, we have demonstrated that relative BFi (rBFi) can be extracted by DCS-NET with a much lower error of 8.35%. By contrast, the semi-infinite and three-layer fitting models result in significant errors in rBFi of 43.76% and 19.66%, respectively. DCS-NET can robustly quantify blood flow measurements at considerable source-detector distances, corresponding to much deeper biological tissues. It has excellent potential for hardware implementation, promising continuous real-time blood flow measurements.

Forecasting carbon price using signal processing technology and extreme gradient boosting optimized by the whale optimization algorithm

AbstractPredicting carbon prices is crucial for the growth of China's carbon trading industry. This paper proposes a residual correction model that considers multiple influencing factors. First, the best historical data and main external factors input by the model are determined by using the partial autocorrelation function and Spearman correlation analysis, and the carbon price forecasting index system is constructed. Second, the whale optimization algorithm (WOA) is utilized to determine the optimal parameters of the extreme gradient boosting (XGBoost), and the WOA‐XGBoost model is built to perform preliminary carbon price forecasts and obtain the residual series. Finally, the carbon price residual series undergoes decomposition into multiple components utilizing the complete ensemble empirical mode decomposition for subsequent forecasting and the aggregation of outcomes. Experiments are conducted to predict two carbon trading markets in Hubei and Guangzhou, and a feature importance analysis is performed. The results indicate that the proposed hybrid model consistently outperforms the comparative models in terms of prediction accuracy. Furthermore, it is revealed that historical carbon prices and European Union carbon prices are the key factors influencing the prediction of carbon market prices.

Synchronization of complexity enhanced chaos in semiconductor lasers

In synchronized chaotic lasers based secure key distribution and other encrypted communications, presence of the time delay signature in chaos poses a threat to security. So the transmitter and receiver lasers should preferably be operated in complexity enhanced chaotic regime where the time delay signature is hidden. However, achieving good synchronization in experiments in such regime is challenging. We report experimental demonstration of achieving excellent synchronization between two semiconductor lasers even when both the lasers are operating in complexity enhanced chaotic regime with absolutely no time delay signature present in their output. This chaotic regime is ensured by evaluating the auto correlation function, permutation entropy and spectrum analysis of the time series. As a measure of synchronization, cross-correlation coefficient of 0.923 is achieved between the transmitter and receiver lasers. This results are of immense importance in chaos based secure key distribution and other encrypted communication schemes.

Analysis of Velocity Autocorrelation Functions from Molecular Dynamics Simulations of a Small Peptide by the Generalized Langevin Equation with a Power-Law Kernel.

Internal motions play an essential role in the biological functions of proteins and have been the subject of numerous theoretical and spectroscopic studies. Such complex environments are associated with anomalous diffusion where, in contrast to the classical Brownian motion, the relevant correlation functions have power law decays with time. In this work, we investigate the presence of long memory stochastic processes through the analysis of atomic velocity autocorrelation functions. Analytical expressions of the velocity autocorrelation function spectrum obtained through a Mori-Zwanzig projection approach were shown to be compatible with molecular dynamics simulations of a small helical peptide (8-polyalanine).

Topography measurement methods evaluation for entire bending-fatigued fracture surfaces of specimens obtained by explosive welding

In this paper, the methods of compensation of differences in the results of entire bending-fatigued fracture surface topographies were presented. The roughness evaluation was performed with a focus variation microscope and confocal surface topography measurement techniques. The differences in the ISO 25178 roughness parameters were investigated and procedures for their compensation were studied. It was found that various types of optical measurements can cause differences in the errors occurring in the measurement process, such as outliers, and noise. The reduction of differences in the various optical roughness measurements can be attained when measurement errors are compensated. For this study, the applications of general procedures available in commercial software can be suitable for improvements of the roughness measurement results, such as raw data thresholding technique, digital filtering (S-filter), power spectral density, and autocorrelation function analyses. The validation of measurement techniques was proposed for areal and profile studies, including analysis of differences in the calculation areal ISO 25178 roughness parameters.

Predicting Potential Evapotranspiration for Kalaburagi District using a Seasonal Arima Model

Forecasting potential evapotranspiration (PET) is of great importance in effectively managing irrigation systems. This article centers around models designed to simulate future PET levels for the Kalaburagi district. The study calculates potential evapotranspiration using temperature data in degrees Celsius, employing the Thornthwaite method, and prediction is performed using the Seasonal Autoregressive Moving Average (SARIMA) method. These models are developed based on autocorrelation function (ACF) and partial autocorrelation function (PACF) analysis. Model selection is based on minimizing Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) values. The chosen models for different stations in Kalaburagi, Chincholi, Sedam, Chittapur, Aland, Jewargi, and Afzalpur respectively are SARIMA (1,0,1)(2,1,0)12, SARIMA(1,0,1)(2,1,0)12, SARIMA(1,0,0)(2,1,0)12, SARIMA(1,0,1)(2,1,0)12, SARIMA (1,0,1) (2,1,0) 12, and SARIMA(1,0,1)(2,1,0)12. The results indicate that the models developed for Jewargi and Chincholi stations show particular promise compared to the other two stations, with all four models performing well. These models have the potential to significantly enhance decision-making in irrigation planning and command area management practices, contributing to improved water resource management.

Desertification simulation using wavelet and box-jenkins time series analysis based on TGSI and albedo remote sensing indices

Desertification has been listed as one of the most critical global environmental issues, posing a significant threat to life, particularly in arid and semiarid regions. Therefore, gaining a comprehensive understanding of the present and future desertification trends becomes imperative. This study employs a feature space model, which effectively captures land surface changes related to desertification, enabling the extraction of pertinent information. Subsequently, time series models are used to determine the most accurate desertification simulation. Twenty-one ETM + sensor images were utilized to calculate the Topsoil Grain Size (TGSI) and Albedo remotely sensed indexes. Constructing the Albedo-TGSI feature space, the Desertification Degree Index (DDI) was extracted for each year. Different levels of desertification were identified by applying a natural break classification on the DDI values, and corresponding break values were obtained. The representative desertification degree for each year was determined by calculating the average of the minimum and maximum break values, resulting in the generation of five distinct time series for five desertification degrees. Different ARIMA models and wavelet transforms were selected to simulate the various desertification degrees based on the analysis of autocorrelation and partial autocorrelation functions and trial and error, respectively. The most suitable ARIMA models with the lowest errors were identified as follows: ARIMA (1,0,7) for severe desertification, ARIMA (0,1,6) for high desertification, ARIMA (0,0,7) for moderate desertification, and ARIMA (3,0,6) for non-desertification degrees. Among the various wavelet transform families tested, the Symlet family proved to be the most effective, except for the low desertification degree. The following wavelet transforms yielded the best results for each degree of desertification: Symlet3 for severe desertification, Symlet7 for high desertification, Symlet7 for moderate desertification, Daubechies 5 (db5) for low desertification, and Symlet7 for non-desertification degree simulations, all exhibiting the minimum error rates.

Resonance Light-Scattering Correlation Spectroscopy and Its Application in Analytical Chemistry for Life Science.

Resonance light-scattering correlation spectroscopy (RLSCS) is a new single-particle detection method with its working principle being like fluorescence correlation spectroscopy (FCS). RLSCS is obtained by autocorrelation function analysis on the measured fluctuation of the resonance light scattering (RLS) intensity occurring within a subfemtoliter volume when a single nanoparticle (such as gold nanoparticles (NPs) or silver (SNPs)) freely diffuses through the volume. The RLSCS technique can detect such parameters as concentration, diffusion coefficient (translation and rotation), etc. Compared with the FCS technique, the correlated fluorescence intensity signal in RLSCS is replaced with the RLS signal of the nanoparticles, overcoming some limits of the fluorescent probes such as photobleaching under high-intensity or long-term illumination. In this Account, we showcase RLSCS methods, theoretical models at different optical configurations, and some key applications. First, the RLSCS optical detection system was constructed based on the confocal optics, its theoretical model was proposed, and the diffusion behaviors of the nanoparticles in the solution were studied including the rotational and translational diffusion. And, methods were developed to measure the concentration, size, aspect ratio, and size distribution of the NPs. Second, based on the RLSCS methods, some detection strategies were developed for homogeneous DNA detection, immunoassay, apoptosis assay, self-thermophoresis of the nanomotor, and quantitative assay in single living cells. Meanwhile, a new fluorescence/scattering cross-correlation spectroscopy (FSCCS) method was proposed for monitoring the molecule-particle interaction. This method enriched the conventional fluorescence/fluorescence cross-correlation spectroscopy (FCCS) method. Third, using the EMCCD with high sensitivity and rapid response as an optical detector, two temporospatially resolved scattering correlation spectroscopy methods and their theoretical models were developed: total internal reflection (TIR) configuration-based spatially resolved scattering correlation spectroscopy (SRSCS) and dark-field illumination-based scattering correlation spectroscopy (DFSCS). These methods extended single-spot confocal RLSCS to imaging RLSCS, which makes RLSCS have the ability for multiple channel detection with temporospatial resolution. The method was successfully used for investigating the dynamic behaviors of gold NPs in live cells and obtained its temporospatial concentration distribution and diffusion behaviors. The final section of this Account outlines future directions in the development of RLSCS.

Sedimentary P- and S-Wave Velocity Structures in Shimousa Region of Kanto Basin Determined from Joint Autocorrelation and Receiver Function Analysis

ABSTRACT To determine the P- and S-wave velocities (VP and VS, respectively) of the sedimentary layers in the Shimousa region of the Kanto basin, Japan, the autocorrelations of P and S waves and the receiver function (RF) for the local earthquakes at the strong-motion stations in the region were jointly analyzed. Because the autocorrelations and RF were insensitive to the event location, the stacked functions for various events captured clear P and S reflections and the Ps phase at the bedrock of the basin. The PpPs phase was also clearly observed at some stations in the region. The arrival times of the P and S reflections and the Ps phase depended on the station. These phases arrived earlier at the northern and eastern parts of the region, and later at the southern and western parts. This trend shows good agreement with that expected from the 3D velocity structure model developed by the Japan Seismic Hazard Information Station. The VP, VS, and thickness (H) values were then estimated from the histogram of the H–V stack for the P and S autocorrelations and the Ps and PpPs phases in the RF. VP, which is less sensitive than VS and H, was not always well determined at some stations, whereas VS and H were well estimated with high resolution. It was found that the resolution depends on the station location in the region. This dependence could be caused by the appearance of clear phases in the functions.

Examination of one-dimensional S-wave velocity structure using strong-motion data for high-seismic-intensity area during the 2018 Hokkaido Eastern Iburi earthquake

The Yufutsu Plain, a sedimentary basin surrounded by mountains, is located in the southern part of the Ishikari–Yufutsu Lowlands, Hokkaido, Japan. The Hidaka arc–arc collision zone, located in the eastern part of the Yufutsu Plain, forms the Hidaka Mountain range in central Hokkaido, with the Ishikari–Teichi–Toen Fault Zone of the Ishikari–Yufutsu Lowlands on the west side, which forms part of a major geological boundary that extends in the north–south direction. The 2018 Hokkaido Eastern Iburi earthquake (Mw 6.6) occurred at 03:08 JST on September 6, 2018, in this arc–arc collision zone. The K-NET HKD126 station in Mukawa Town, which is close to the severely damaged basin margin area, recorded strong-motion data with strong power for a predominant frequency of 0.5–1.0 Hz during the main shock. The peak ground acceleration was 661 cm/s2 in the east–west direction. The site amplification characteristics of the shallow S-wave velocity structure, which was estimated from microtremor array observations and surface wave explorations, were one of the causes of this strong ground motion. It is essential to accurately estimate the depth of the seismic bedrock and basin margin to evaluate the long period of large earthquakes. In this study, we used strong-motion data recorded at HKD126 and three temporary strong-motion stations near the basin margin area to tune the deep S-wave velocity structure. First, we performed microtremor array observations and surface wave explorations to estimate the S-wave velocity structure to a depth of 1 km beneath the station at the hill site because a detailed shallow structure is not available for this site. Then, with a combination of the estimated S-wave velocity structure and the existing structure, we tuned the deep structures based on an autocorrelation function analysis using strong-motion data. The validity of the estimated structures from the shallowest depth to the seismic bedrock was verified based on the differences between the observed arrival time difference and theoretical travel time difference for the S-wave initial motion. We estimated the seismic bedrock of the four stations to be at a depth of 7–10 km. In addition, an autocorrelation function analysis suggests topological bedrock undulations.Graphical

A theoretical and experimental investigation into surface generation in ultra-precision diamond milling

Ultra-precision diamond milling (UPDM) provides a promising generation of high-quality surface up to sub-micrometric form accuracy and nanometric surface roughness. Prior to its machining process, the investigation on surface generation would be beneficial to achieve desired quality with reduced cost and boosted productivity. However, few studies discussed this issue so far. In this study, a theoretical and experimental investigation into surface generation was carried out in UPDM. Firstly, a geometric model was built up considering the material removal process between the milling tool and the workpiece. Secondly, surface generation process was elaborated according to the developed model. Finally, UPDM experiments were performed on a typical brass material at different cutting conditions and surface texture parameters were characterized according to ISO 25178-2. Autocorrelation function (ACF) analysis was employed for a detailed evaluation of surface generation. The results showed that the static factors (cutting parameters) as well as the dynamic factors (material effects and spindle vibration), which were associated with the cutting conditions, yielded a great influence on surface generation. Surface texture characterization indicated that there was a good consistence between simulation and experiment, demonstrating the feasibility of the proposed method. ACF analysis indicated that, with the increased feedrate/step ratio, surface generation approximately achieved a transition from the periodical surface (dominated by cutting residuals) to the random surface (determined by multiple components). Significantly, this study draws up a fundamental understanding toward surface generation in UPDM.

Onset of collective excitations in the transverse dynamics of simple fluids.

A thorough analysis of the transverse current autocorrelation function obtained by molecular dynamics simulations of a dense Lennard-Jones fluid reveals that even such a simple system is characterized by a varied dynamical behavior with changing length scale. By using the exponential expansion theory, we provide a full account of the time correlation at wavevectors Q between the upper boundary of the hydrodynamic region and Q_{p}/2, with Q_{p} being the position of the main peak of the static structure factor. In the Q range studied, we identify and accurately locate the wavevector at which shear wave propagation starts to take place, and show clearly how this phenomenon may be represented by a damped harmonic oscillator changing, in a continuous way, from an overdamped to an underdamped condition. The decomposition into exponential modes allows one to convincingly establish not only the crossover related to the onset of transverse waves but, surprisingly, also the existence of a second pair of modes equivalent to another oscillator that undergoes, at higher Q values, a similarly smooth over to underdamped transition.

Toothpaste-related interests of Google users from different countries.

The Internet is a growing source of knowledge and can provide information about oral health. This ecological study aimed to characterize the interests in toothpaste among Google users from different countries. Our hypothesis was that there would be an increase in Google users' interest in information about toothpaste. This retrospective longitudinal ecological study analyzed the toothpaste-related interest of Google users from 10 countries between January 2004 and December 2020. The monthly variation in relative search volume (RSV) and the main related queries were determined using Google Trends. Autoregressive integrated moving average (ARIMA) forecasting models were built to establish the predictive RSV values for toothpaste for an additional 12 months. Autocorrelation plots and the generalized additive model (GAM) were used to diagnose trends and seasonality in RSV curves. Additionally, the influence of social isolation related to the outbreak of COVID-19 was analyzed. Although not detected by autocorrelation function (ACF) and partial autocorrelation function (PACF) analyses, the heuristic analysis showed an increase in the interest in toothpaste-related information in all countries, with a stable trend observed in the 12-month forecasts, except for the increases in the United Kingdom and South Africa. Also, GAM analyses demonstrated a non-significant monthly or quarterly seasonal influence on data. In addition, social isolation during the COVID-19 pandemic did not influence the online information-seeking behavior of Google Search users linked to this topic. We confirmed the hypothesis that the interest of Google Search users in information about toothpaste increased in all of the 10 assessed countries.

Variable Daily Autocorrelation Functions of High-Frequency Seismic Data on Mars

AbstractHigh-frequency seismic data on Mars are dominated by wind-generated lander vibrations, which are radiated partially to the subsurface. Autocorrelation functions (ACFs) of seismic data on Mars filtered between 1 and 5 Hz show clear phases at ∼1.3, ∼2.6, and ∼3.9 s. Daily temporal changes of their arrival times (dt/t) correlate well with the daily changes of ground temperature, with ∼5% daily variation and ∼50 min apparent phase delay. The following two mechanisms could explain the observations: (1) the interference of two predominant spectral peaks at ∼3.3 and ∼4.1 Hz, assumed to be both lander resonance modes, generate the apparent arrivals in the ACFs; (2) the interference of the lander vibration and its reflection from an interface ∼200 m below the lander generate the 3.3 Hz spectral peak and ∼1.3 s arrival in the ACFs. The driving mechanism of the resolved dt/t that most likely explains the ∼50 min delay is thermoelastic strain at a near-surface layer, affecting the lander–ground coupling and subsurface structures. The two outlined mechanisms suggest, respectively, up to ∼10% changes in ground stiffness at 1–5 Hz and ∼15% velocity changes in the top ∼20 m layer. These are upper bound values considering also other possible contributions. The presented methodology and results contribute to analysis of ACFs with limited data and the understanding of subsurface materials on Mars.

Chaos arising from the hydrological behaviour of a floodplain river during the last century

AbstractThe hydrological regime is the main factor governing the functioning of floodplain rivers. A full comprehension of its dynamic leads to a better understanding of the system's behaviour. We analysed the daily water level of the Paraná River during the last century at three gauge stations using linear and non‐linear tools to characterise the hydrological dynamic and to analyse to what extent chaotic behaviour prevails. The three water level time series were characterised as non‐linear and non‐stationary by power spectrum, autocorrelation function, and surrogate test analyses. A strange attractor was developed when the phase space was reconstructed, having a low dimensional chaos supported by correlation dimension, positive maximum Lyapunov exponents, and recurrence quantification analysis. The sample entropy analysis shows that the system resulted unpredictable beyond a temporal threshold, and with an intermediate hydrological complexity, while Hurst exponent characterised it as persistent and with sensitive dependence on initial conditions. In a general overview, all the evidence obtained indicates that the Paraná River's behaviour is at the edge of chaos. A latitudinal gradient of decreasing chaoticity was observed as the floodplain extent increased, whereas complexity was highest at the intermediate river station due to the inflow of tributaries with different hydrology. This paper attempts to offer some additional insights for understanding the hydrological behaviour of floodplain rivers and the most appropriate methods to understand their complexity.

COVID-19 and domestic trade in Bulgaria

Domestic trade is an essential contributor to economic growth and an indicator of the people’s welfare. It is vulnerable to the COVID-19 crisis due to the pandemic itself and the government’s measures against it. An accurate estimation of the pandemic influence on domestic trade is needed for effective economic intervention in support of the economic recovery and improvement of the well-being of the population. The aim of this paper is to estimate the magnitude and timing of the COVID-19 impact on domestic trade in Bulgaria. The data used in the study covered the period 2000–2020 with monthly data for the indicator “Turnover for wholesale and retail trade and repair of motor vehicles and motorcycles in Bulgaria.” This paper employed unit root tests, autocorrelation function analysis, building, estimating, forecasting ARIMA and ARCH models, and intervention analysis. The results revealed that Bulgarian domestic trade followed the difference-stationary process as unit root tests failed to reject the random walk hypothesis. The COVID-19 impact on domestic trade proved to be long-lasting and has permanently decreased its level since March 2020. The timing of the impact coincided with the government’s measures against the pandemic. The drop in the volume of domestic trade was substantial and estimated at 19.3%. Following the nature of domestic trade, determined and decisive intervention is necessary if the Bulgarian government seeks to expand domestic demand and successfully procure economic recovery.

Autocorrelation function of finite-length data in fluorescence correlation spectroscopy

The experimental autocorrelation function of fluorescence correlation spectroscopy calculated from finite-length data is a biased estimator of the theoretical correlation function. This study presents a new theoretical framework that explicitly accounts for the data length to allow for unbiased analysis of experimental autocorrelation functions. To validate our theory, we applied it to experiments and simulations of diffusion and characterized the accuracy and precision of the resulting parameter estimates. Because measurements in living cells are often affected by instabilities of the fluorescence signal, autocorrelation functions are typically calculated on segmented data to improve their robustness. Our reformulated theory extends the range of usable segment times down to timescales approaching the diffusion time. This flexibility confers unique advantages for live-cell data that contain intensity variations and instabilities. We describe several applications of short segmentation to analyze data contaminated with unwanted fluctuations, drifts, or spikes in the intensity that are not suited for conventional fluorescence correlation analysis. These results demonstrate the potential of our theoretical framework to significantly expand the experimental systems accessible to fluorescence correlation spectroscopy.

ARIMA MODEL FOR FORECASTING THE BITCOIN EXCHANGE RATE AGAINST THE USD

This study analysis forecasting the bitcoin exchange rate against the USD. The dataset selected for this study starts from January 2015 to June 2022. This study's methodology uses autoregressive integrated moving average forecasting (ARIMA). The overall outcomes of this study were gathered from the statistical software Minitab 21.1. The Box Jenkins approaches are also used to predict the best model. To determine the ARIMA model parameter, this study did autocorrelation function (ACF) and partial autocorrelation function (PACF) analyses. According to the Box-Cox transformation method, log transformation was selected. The outcome demonstrates that the seasonal with the regular difference in the Bitcoin exchange rate against the USD is a stationary data series. The forecasting model used in this study is ARIMA (1,1,0) (2,1,1)12. This predicted model is identified through the Mean squared error by comparing the other guessing ARIMA models. After the prediction, 5 Month bitcoin exchange rate against the USD. Investors will be able to estimate the bitcoin exchange rate against the USD with the use of this information, but volatility must also be properly watched. This will aid investors in making better investment decisions and increase profits. In future studies, better consider another exchange rate of BTC and software experts will develop such type of software based on ARIMA models for prediction.