6. Statistical and Time-Series Analytics

Introduction and Context

IoT systems generate data continuously. Temperature sensors in a cold-storage facility, vibration sensors on industrial motors, smart meters in buildings, and GPS devices in logistics fleets all produce observations indexed by time. Unlike many conventional business datasets, IoT data is often high-volume, irregular, noisy, incomplete, and strongly influenced by operating conditions. The analytical task is therefore not simply to calculate an average or fit a predictive model. It is to determine what the data represents, identify the structure embedded in it, distinguish meaningful changes from measurement artefacts, and communicate uncertainty to those responsible for operational decisions.

Statistical and time-series analytics provide the foundation for this work. Statistical analysis describes variation, dependence, probability, and relationships among variables. Time-series analysis additionally considers the order in which observations occur. This ordering is essential: a sensor reading at 10:00 may be related to the reading at 09:59, and a sudden change may indicate either a genuine event or a faulty sensor. Consequently, methods designed for independent observations can produce misleading results when applied directly to telemetry streams.

This chapter develops a practical and conceptual framework for analysing IoT sensor and telemetry data. It covers exploratory analysis, probability models, signal processing, smoothing, decomposition, forecasting, change-point detection, and uncertainty assessment. It also considers deployment issues, governance, and the professional judgement required when analytical outputs influence maintenance, safety, energy management, or service quality.

Learning Objectives

By the end of this chapter, the learner should be able to:

1. Explain the distinctive statistical properties of IoT and sensor data.

2. Conduct exploratory analysis of temporal, multivariate, and event-driven data.

3. Select appropriate probability models and interpret statistical distributions.

4. Apply filtering, smoothing, decomposition, and signal-processing techniques.

5. Distinguish trend, seasonality, cycles, noise, and anomalous behaviour.

6. Build and evaluate suitable time-series forecasting models.

7. Detect and interpret changes in the statistical behaviour of a data stream.

8. Quantify uncertainty and communicate the limitations of analytical conclusions.

9. Design an analytical workflow suitable for operational IoT deployment.

The Statistical Character of IoT Data

A sensor observation is not merely a number. It is a measurement produced by a device, under particular environmental and operational conditions, using a specified unit, sampling process, calibration state, and communication pathway. A useful analytical record commonly contains a timestamp, device identifier, variable name, value, unit, quality indicator, and contextual attributes such as location or machine state.

Several characteristics distinguish IoT data from simpler tabular data. First, observations are ordered in time and may be autocorrelated. Second, sampling may be regular, event-driven, delayed, or irregular. Third, data may contain missing intervals caused by network outages or device sleep modes. Fourth, sensors can drift, saturate, duplicate readings, or transmit values outside their physical range. Fifth, the distribution of a variable may change according to a regime, such as machine idle, startup, normal production, or overload.

The distinction between a data error and a rare but valid event is especially important. A temperature reading of 150°C may be impossible for a room sensor but plausible for a furnace sensor. A value that appears extreme in the overall dataset may be normal during a particular operating state. Therefore, data quality rules should combine physical knowledge, historical behaviour, device metadata, and statistical evidence.

Important Terminology

A time series is a sequence of observations indexed by time. Sampling interval is the time between successive scheduled observations. Temporal resolution describes the granularity at which changes can be observed. Autocorrelation measures dependence between observations separated by a particular lag. Lag is the time displacement between two observations. Stationarity refers to a process whose statistical properties remain stable over time, at least in the sense required by a selected model. Trend is a persistent long-term movement. Seasonality is a regular pattern associated with a known calendar or operational period. Cycle is a longer or less regular oscillation. Noise is random or unstructured variation. Residual is the part left after an explanatory model has been fitted.

A change point is a time at which the statistical properties of a process change. A regime is a period characterised by relatively stable operating behaviour. Forecast horizon is the future period for which predictions are made. A prediction interval represents uncertainty about a future observation, whereas a confidence interval generally describes uncertainty about an estimated parameter or expected value. Concept drift occurs when relationships between inputs and outcomes change over time, potentially reducing model performance.

Exploratory Analysis: From Raw Telemetry to Interpretable Evidence

Exploratory data analysis should begin with a data audit rather than a model. Analysts should establish the time zone, timestamp precision, expected sampling frequency, device identity, units, valid ranges, and known maintenance periods. Duplicate timestamps, out-of-order records, negative durations, and inconsistent units can create patterns that have no physical meaning.

Descriptive statistics such as mean, median, standard deviation, interquartile range, minimum, and maximum provide an initial view of location and variability. For skewed data, the median and quantiles are usually more informative than the mean. A histogram or empirical cumulative distribution can reveal multimodality, truncation, heavy tails, or saturation. Box plots can compare distributions by device, site, shift, or operating state, but they should not replace temporal displays.

Time plots are central to IoT analysis. A line plot can reveal drift, periodicity, bursts, missing intervals, and abrupt transitions. Plotting several variables on a common time axis helps identify lead-lag relationships. Scatter plots and correlation matrices are useful, but correlation must be interpreted cautiously. Two sensors may correlate because both respond to ambient temperature, because one is derived from the other, or because both follow a shared daily schedule.

For temporal dependence, autocorrelation and partial autocorrelation plots can help identify lag structure. Aggregating data at different resolutions may reveal patterns hidden in high-frequency noise. For example, minute-level energy readings may appear erratic, while hourly totals reveal a stable workday pattern. Aggregation, however, can also conceal short-lived safety events, so the appropriate resolution depends on the decision being supported.

Exploration should be stratified by context. A motor’s vibration distribution during idle operation should not be compared uncritically with its distribution under full load. Useful contextual fields include machine state, production batch, weather, operator shift, firmware version, and maintenance status. In advanced IoT systems, exploratory analysis is therefore both statistical and semantic: the analyst must understand what the device and its operating environment mean.

Probability Models for Sensor and Event Data

Probability models provide a language for uncertainty and variation. A continuous measurement such as temperature or pressure may be represented by a probability density, while an event such as an alarm within an hour may be represented by a Bernoulli or binomial variable. The model should be selected because it reflects the data-generating mechanism, not merely because it is familiar.

The normal distribution is often useful as an approximation for measurement noise around a stable operating point. It is less appropriate when values are bounded, strongly skewed, multimodal, or generated by several operating regimes. A log-normal model may describe positive variables whose logarithms are approximately normal, such as certain duration or concentration measurements. Gamma models are useful for positive, skewed quantities, including waiting times and some consumption measures.

For counts, Poisson models are a starting point when events occur independently at a relatively stable rate. If the variance substantially exceeds the mean, overdispersion may suggest a negative binomial model or an unobserved mixture of rates. Binary outcomes can be modelled with Bernoulli or logistic models. For repeated sensor states, Markov models can represent the probability of moving from one state to another, such as normal, warning, and failure-proximate conditions.

IoT data frequently violates independence assumptions. Repeated observations from the same device are correlated, and devices may differ systematically. Hierarchical or mixed-effects models can represent both population-level effects and device-specific variation. For example, a model may estimate the overall effect of ambient temperature on energy consumption while allowing each building to have its own baseline.

Model checking is more important than mechanical distribution fitting. Analysts should inspect residuals, compare observed and expected quantiles, test sensitivity to alternative assumptions, and consider whether the model remains appropriate across operating regimes. A statistically convenient model that ignores sensor saturation or changing variance may produce precise but unreliable conclusions.

Signal Processing and Smoothing

Sensor signals commonly contain high-frequency noise superimposed on a slower operational pattern. Signal processing aims to separate meaningful structure from unwanted variation while preserving events that matter. The choice of method depends on the frequency characteristics of the process and the cost of missing a transient event.

A moving average replaces each observation with the average of nearby observations. It is simple and useful for visualisation or reducing random noise, but it introduces lag and can blur peaks. A weighted moving average gives greater importance to recent observations. Exponential smoothing assigns declining weights to older observations and is particularly suitable for online systems because it can be updated incrementally.

The smoothing parameter controls responsiveness. Strong smoothing produces a stable signal but reacts slowly to genuine changes; weak smoothing responds quickly but retains more noise. This is an operational trade-off. In a safety system, excessive smoothing may delay an alarm. In energy reporting, stronger smoothing may be acceptable because the objective is to estimate an underlying consumption pattern rather than detect a brief spike.

Median filters are effective against isolated spikes because they are less sensitive to extreme values than means. Low-pass filters attenuate rapid fluctuations, while high-pass filters emphasise rapid changes. Band-pass filters isolate a frequency range and can be valuable in vibration analysis. In industrial applications, frequency-domain tools such as the Fourier transform can identify dominant periodic components, although interpretation requires attention to sampling frequency, aliasing, windowing, and non-stationarity.

A common mistake is to treat filtering as neutral preprocessing. Every filter changes the signal. Analysts should document the window size, filter type, boundary handling, and whether the filtered value was available in real time or calculated retrospectively. Filters that use future observations are unsuitable for real-time prediction unless their operational delay is explicitly accepted.

Decomposition: Understanding What Produces the Observation

A useful conceptual model represents an observed series as the combination of systematic and irregular components. In an additive decomposition,

Y_t = T_t + S_t + R_t,

where T is trend, S is seasonal structure, and R is the remainder. In a multiplicative decomposition,

Y_t = T_t × S_t × R_t,

which is appropriate when seasonal variation increases with the level of the series. A logarithmic transformation can sometimes convert multiplicative behaviour into an additive form.

Trend describes persistent movement, such as gradual battery degradation. Seasonality may arise from daily occupancy, weekly production schedules, or annual weather patterns. Cycles are longer and often less predictable than seasonality; they may reflect economic conditions, maintenance cycles, or changing production demand. The remainder includes random variation, unmodelled effects, measurement noise, and potentially anomalies.

Classical decomposition is transparent but can be sensitive to missing values and changing seasonal patterns. More flexible approaches, such as locally weighted regression and robust seasonal-trend decomposition, can accommodate outliers and evolving patterns. Decomposition should be interpreted as a modelling choice, not as a physical truth. A component identified as “seasonal” may actually represent an unmeasured operational schedule.

Decomposition is useful for diagnosis. If residuals remain autocorrelated, the model has not captured all temporal structure. If residual variance increases with the level, transformation or a different error model may be required. If apparent seasonality disappears after controlling for machine state, the original pattern was contextual rather than intrinsic.

Forecasting Sensor and Telemetry Streams

Forecasting estimates future values or future events using historical information and relevant explanatory variables. The forecasting objective must be stated precisely. Predicting the next five minutes of motor temperature is different from predicting tomorrow’s energy demand or estimating the remaining useful life of a battery.

A forecasting workflow begins with a time-ordered split. Randomly shuffling observations allows information from the future to enter the training set and produces optimistic evaluation. Baselines are essential. A naïve forecast may use the last observation; a seasonal naïve forecast may use the value from the previous day or week. A complex model should demonstrate improvement over these simple references.

Exponential smoothing models are effective for series with level, trend, and seasonality. Autoregressive models use previous observations, while moving-average terms model dependence on previous errors. ARIMA-type models can be appropriate after differencing or other transformations have made the series sufficiently stable. Seasonal extensions incorporate repeating lag structures.

Regression with lagged variables and external predictors is useful when temperature, occupancy, production volume, or machine load influence the target. State-space models provide a flexible framework for time-varying levels, trends, and uncertainty. Machine-learning methods, including tree ensembles and neural networks, may capture nonlinear relationships, but they require careful feature construction, temporal validation, monitoring, and interpretability controls.

Forecast quality should be evaluated at the decision-relevant horizon. Mean absolute error is readily interpretable; root mean squared error gives greater weight to large errors; percentage-based metrics can be problematic when actual values approach zero. Quantile forecasts and prediction intervals are often more useful than a single point estimate because operational decisions involve risk. Calibration asks whether intervals contain the true outcome at approximately their stated frequency.

Forecasting failure often results from data leakage, unrecognised regime changes, unstable sensors, or a mismatch between the model horizon and the operating decision. A model that performs well during normal operation may be unsafe during startup or fault conditions. Evaluation should therefore include stress periods and separate analysis by regime.

Change-Point Detection and Anomaly Interpretation

An anomaly is an observation or pattern that differs from an expected baseline. A change point is a transition in the underlying distribution, mean, variance, trend, or dependence structure. The distinction matters: an isolated spike may be a transient anomaly, whereas a sustained shift may indicate recalibration, environmental change, degradation, or a new operating regime.

Statistical process-control charts provide a practical framework. A Shewhart chart is sensitive to large, sudden deviations. Cumulative-sum methods accumulate small deviations and can detect gradual shifts. Exponentially weighted moving-average charts give more emphasis to recent data. Thresholds should be based on a stable reference period and adjusted for autocorrelation where necessary.

Window-based methods compare statistics before and after a candidate time. A change in mean may be detected using likelihood ratios, cumulative statistics, or non-parametric comparisons. Bayesian approaches can estimate the probability that a change has occurred, while online algorithms are designed for streaming data and limited computational resources.

An alert is not automatically an incident. Alert logic should consider persistence, magnitude, corroboration by other sensors, operating state, and consequences. A single temperature spike accompanied by a communication-quality warning may indicate a faulty reading. The same spike, confirmed by pressure and vibration signals, may justify immediate intervention. Alert fatigue is a serious organizational risk; excessive false positives cause personnel to ignore future warnings.

Uncertainty Assessment and Decision Use

Uncertainty enters IoT analytics through measurement error, missing data, parameter estimation, model selection, future randomness, and changing conditions. A responsible analytical system makes these sources visible rather than presenting a forecast as a fact.

Confidence intervals describe uncertainty about estimated quantities under specified assumptions. Prediction intervals are wider because they include uncertainty about a future observation. Bootstrapping can estimate uncertainty without relying entirely on a particular distributional form, although temporal dependence requires block or time-series bootstrap methods rather than naïve resampling of individual observations.

Sensor uncertainty should be distinguished from model uncertainty. A calibrated sensor may have a known measurement tolerance, while a forecasting model may be uncertain because future operating conditions are unknown. Combining these sources requires care. In high-consequence applications, analysts should conduct sensitivity analysis, scenario analysis, and worst-case assessment.

Decision thresholds should reflect the costs of different errors. In predictive maintenance, a false alarm may incur an inspection cost, whereas a missed failure may cause injury, downtime, or environmental harm. The preferred threshold is therefore not necessarily the one that maximises statistical accuracy. It should be linked to a documented loss function, escalation procedure, and human review process.

An Applied Case: Predictive Monitoring of an Industrial Pump

Background

The following is an illustrative case. A water-treatment facility operates several electrically driven pumps. Each pump reports discharge pressure, motor current, vibration amplitude, temperature, and operating state at one-minute intervals. Maintenance is currently scheduled by fixed calendar intervals, but unplanned pump failures have caused service interruptions.

Situation and Problem

Engineers observe that some pumps develop increased vibration several days before failure, but the raw vibration series is noisy and affected by pump load. The facility wants an early-warning system that identifies deterioration without producing excessive false alarms.

Analysis

The analytical team first audits timestamps, sampling continuity, units, sensor ranges, and maintenance records. Intervals during planned shutdowns are labelled rather than treated as missing at random. Exploratory plots show three operating regimes: idle, normal flow, and high flow. Vibration is substantially higher during high flow, so a single unconditional threshold would be inappropriate.

The team applies a short median filter to reduce isolated spikes and an exponential smoother for online monitoring. Separate baseline distributions are estimated for each operating regime. Residual vibration is then calculated relative to expected vibration conditional on motor current and pump state. Autocorrelation indicates that observations remain dependent over several minutes, so consecutive threshold crossings are treated as one episode rather than independent alarms.

A change-point procedure is applied to the residual series. The system requires evidence of a sustained upward shift and corroboration from motor current or temperature. Forecasting is used to estimate vibration over the next 24 hours, with prediction intervals. A warning is generated when the forecast distribution places substantial probability above the maintenance threshold, while a critical alert requires corroboration and a shorter expected time to exceedance.

Approach and Solution

The final workflow combines:

• regime-aware exploratory analysis;
• robust filtering of isolated measurement spikes;
• baseline modelling conditional on operating state;
• online change-point detection;
• short-horizon probabilistic forecasting; and
• human review linked to a maintenance work-order system.

The dashboard displays the current measurement, smoothed signal, baseline deviation, confidence or prediction band, operating regime, and evidence supporting the alert. Analysts retain raw values for auditability and never overwrite them with filtered data.

Outcome

The approach improves interpretability because maintenance staff can see whether an alert reflects a genuine deviation from comparable operating conditions. It also reduces alert fatigue by requiring persistence and corroboration. The facility continues to review false negatives and false positives, recalibrates baselines after major repairs, and monitors whether the sensor relationship changes after firmware updates.

Learning Points

The case illustrates that effective IoT analytics is rarely a single algorithm. Contextual segmentation, signal processing, temporal dependence, uncertainty, and operational workflow must be designed together. A statistically strong detector can still fail if its alert is not actionable, if maintenance data is incomplete, or if users cannot distinguish a sensor fault from equipment deterioration.

Challenges, Risks, and Common Mistakes

A frequent error is applying ordinary statistical tests that assume independent observations to strongly autocorrelated data. Another is using random train-test splits for forecasting. Analysts also confuse correlation with causation, interpret smoothing as evidence of a real trend, and remove outliers without investigating their physical meaning.

Missing data requires diagnosis. Network loss, device failure, scheduled sleep, and values missing because a sensor exceeded range have different implications. Imputation may be reasonable for short gaps in a smooth monitoring series, but it can be inappropriate for event detection or failure analysis. Imputed values should be flagged and should not be presented as direct measurements.

Data leakage is particularly damaging. Future values may enter features through centred moving averages, retrospective interpolation, maintenance labels, or aggregate variables calculated over the complete dataset. Reproducibility requires versioned data, documented transformations, fixed time zones, model metadata, and records of alert decisions.

Concept drift is another central risk. A new production process, sensor replacement, climate pattern, or maintenance intervention may change the data-generating process. Models should therefore be monitored using data-quality indicators, forecast errors, calibration measures, and drift statistics. Retraining should be governed rather than triggered blindly by every unusual observation.

Ethical, Governance, and Professional Considerations

IoT analytics can affect worker safety, equipment access, insurance, energy use, and organizational accountability. Data governance should specify ownership, retention, access rights, audit trails, and acceptable uses. Location and occupancy data may reveal personal behaviour even when collected for building management. Aggregation, minimisation, access control, and transparent notices can reduce privacy risk.

Automated alerts should not conceal uncertainty or remove appropriate human responsibility. In safety-critical applications, the analytical system should fail safely, provide understandable evidence, and support independent verification. Models should be tested across sites, devices, and operating regimes to identify unequal performance. Professional practice requires documenting assumptions, known failure modes, threshold rationale, and conditions under which the model should not be trusted.

Technology and Emerging Practice

Modern IoT analytics increasingly combines streaming platforms, time-series databases, edge computing, and cloud-based model management. Edge devices can calculate summaries, filters, and simple anomaly scores locally, reducing latency and bandwidth. More complex forecasting and retraining may occur in the cloud, provided that data transfer, security, and availability requirements are satisfied.

Online learning methods update models as new observations arrive, but continual adaptation can absorb faults or abnormal periods into the baseline. Guardrails, reference windows, and human approval are therefore important. Digital twins can connect sensor streams with engineering models, enabling statistical residuals to be interpreted against expected physical behaviour.

Probabilistic machine learning, conformal prediction, self-supervised representation learning, and hybrid physics-informed models are active areas of development. Their practical value depends not only on predictive performance but also on calibration, computational cost, explainability, and resilience under distribution shift. The central principle remains unchanged: sophisticated analytics must be matched to the measurement process and the decision context.

Best Practices for an IoT Time-Series Workflow

A robust workflow should:

1. Define the operational decision and forecast or detection horizon before modelling.

2. Preserve raw data and record every transformation.

3. Validate timestamps, units, ranges, sampling behaviour, and device identity.

4. Explore data by time, device, location, and operating regime.

5. Establish naïve baselines before adopting complex models.

6. Use time-aware validation and evaluate the periods that matter operationally.

7. Treat missingness, outliers, and sensor faults as analytical questions.

8. Quantify uncertainty and assess calibration, not only point accuracy.

9. Set thresholds according to consequences and costs of errors.

10. Monitor drift, data quality, alert burden, and real-world outcomes after deployment.

Chapter Summary

Statistical and time-series analytics convert continuous IoT measurements into evidence for diagnosis, prediction, and action. Effective analysis begins with a data audit and exploratory investigation of temporal dependence, operating regimes, missingness, and measurement quality. Probability models describe variation and events, while signal-processing methods reduce noise or isolate meaningful frequency components. Smoothing and decomposition help separate level, trend, seasonality, cycles, and residual behaviour.

Forecasting requires time-ordered validation, suitable baselines, regime awareness, and uncertainty intervals. Change-point and anomaly methods should distinguish isolated measurement faults from sustained shifts in system behaviour. Throughout the workflow, uncertainty, cost-sensitive thresholds, governance, and human interpretation are as important as algorithmic accuracy. In professional IoT practice, the best solution is usually an integrated monitoring process rather than a single statistical model.

Key Terms

Autocorrelation: Dependence between observations in a time series at specified lags.

Change point: A time at which the statistical properties of a process alter.

Concept drift: Change over time in the relationship between inputs, outputs, or data distributions.

Decomposition: Separation of a time series into components such as trend, seasonality, and remainder.

Exponential smoothing: A method that assigns decreasing weights to older observations.

Forecast horizon: The future period covered by a forecast.

Lag: The temporal distance between observations used in an analysis.

Moving average: A local average used to smooth a series.

Prediction interval: A range expressing uncertainty about a future observation.

Regime: A period with relatively stable operating or statistical characteristics.

Residual: The difference between an observed value and its model-based expected value.

Seasonality: A recurring pattern associated with a known time or operational period.

Signal processing: Techniques for extracting relevant structure from measured signals.

Stationarity: Approximate stability of a process’s statistical properties over time.

Time series: Observations recorded in temporal order.

Trend: Persistent long-term movement in a series.

Uncertainty: Lack of complete knowledge about measurements, parameters, models, or future outcomes.

Change-point detection: Statistical identification of shifts in a process.

Review Questions

Short Answer Questions

1. Why is temporal ordering important when analysing IoT sensor data?

2. Distinguish between a trend, seasonality, and a cycle.

3. What is the difference between a confidence interval and a prediction interval?

4. Why can a single unconditional threshold be misleading for industrial sensor data?

5. State two risks associated with smoothing sensor data.

Long Answer Questions

1. Explain a complete exploratory analysis workflow for a multivariate IoT time series.

2. Compare moving averages, exponential smoothing, and median filtering in terms of purpose and limitations.

3. Discuss how probability models can be selected for continuous measurements, counts, and binary events.

4. Explain the principles of time-aware forecasting evaluation and the dangers of data leakage.

5. Discuss how uncertainty and decision costs should influence the design of an IoT alerting system.

Analytical / Application Questions

1. A building’s electricity readings show strong daily patterns, increasing variance during working hours, and several missing overnight intervals. Design an analysis plan that addresses decomposition, missingness, and forecasting.

2. A pump’s vibration increases gradually during high-load operation but returns to normal at low load. Explain how you would distinguish load effects, sensor noise, and equipment degradation.

3. A predictive maintenance model produces accurate forecasts but generates too many alarms for operators to review. Propose changes to the analytical and organizational workflow, and justify them using concepts from this chapter.

22. Multiple Choice Questions with Answers

Question 1

Which characteristic most directly distinguishes IoT time-series data from an ordinary unordered dataset?

A. It always contains numerical variables

B. Its observations are temporally ordered and may be dependent

C. It cannot contain missing values

D. Its variables always follow a normal distribution

Correct Answer: B. Its observations are temporally ordered and may be dependent

Question 2

Why should a forecasting dataset generally be split in temporal order rather than randomly?

A. Random splitting removes all seasonality

B. Temporal splitting prevents future information from entering model training

C. Temporal splitting guarantees zero forecast error

D. Random splitting is valid only for categorical data

Correct Answer: B. Temporal splitting prevents future information from entering model training

Question 3

Which method is generally most resistant to isolated extreme spikes in a sensor signal?

A. Simple mean filter

B. Median filter

C. Random interpolation

D. Seasonal decomposition

Correct Answer: B. Median filter

Question 4

A series is best represented by Yt = Tt + St + Rt when seasonal variation is approximately constant in magnitude. What does St represent?

A. The trend component

B. The measurement error only

C. The seasonal component

D. The forecast horizon

Correct Answer: C. The seasonal component

Question 5

A count of alarms has variance much larger than its mean. Which issue should the analyst consider?

A. Overdispersion and a model such as the negative binomial

B. Replacing all counts with continuous normal data

C. Assuming observations are necessarily independent

D. Using a moving average as the probability model

Correct Answer: A. Overdispersion and a model such as the negative binomial

Question 6

What is the main distinction between an isolated anomaly and a change point?

A. An anomaly is always caused by human error

B. A change point indicates a sustained change in process behaviour

C. A change point can occur only in categorical data

D. An anomaly must last longer than a change point

Correct Answer: B. A change point indicates a sustained change in process behaviour

Question 7

Why are naïve forecasts useful in IoT forecasting projects?

A. They provide a baseline against which complex models can be judged

B. They always outperform machine-learning models

C. They eliminate uncertainty intervals

D. They require no time ordering

Correct Answer: A. They provide a baseline against which complex models can be judged

Question 8

Which situation is an example of data leakage?

A. Using a lagged temperature reading to predict current energy use

B. Using a centred moving average that includes future readings in a real-time model

C. Separating training and test data by date

D. Recording the sensor firmware version

Correct Answer: B. Using a centred moving average that includes future readings in a real-time model

Question 9

Why might an alert threshold need to differ between idle and high-load machine states?

A. The unit of measurement changes automatically

B. The expected distribution and baseline behaviour differ by operating regime

C. High-load data cannot be visualised

D. Idle observations are always missing

Correct Answer: B. The expected distribution and baseline behaviour differ by operating regime

Question 10

What does a prediction interval primarily communicate?

A. The exact value that will occur in the future

B. Uncertainty about a future observation

C. The number of sensors in a system

D. Only uncertainty caused by calibration error

Correct Answer: B. Uncertainty about a future observation