Secondary Logo

Journal Logo

Original Research

Time Series Analysis: Evaluating Performance Trends Within Resistance Exercise Sessions

Chiu, Loren ZF; Salem, George J

Author Information
Journal of Strength and Conditioning Research: January 2010 - Volume 24 - Issue 1 - p 230-234
doi: 10.1519/JSC.0b013e3181bd452e
  • Free



Recent technical advances have increased the capabilities of coaches and researchers to collect, analyze, and interpret data during exercise and sports performance (4,9,14). This technology incorporates hardware, such as linear position transducers, accelerometers, and digital video, and software that calculates or estimates biomechanical performance data, including velocity, force, and power. Monitoring performance during an exercise bout can be utilized to adjust acute programming variables, such as volume, intensity, and rest, to maximize performance acutely and/or minimize fatigue (7). Similarly, monitoring performance during a period of training can be utilized to evaluate the effectiveness of the training program. The importance of frequent evaluation is particularly important during periods where training load (i.e., volume, intensity, or both) is high and overtraining is a concern (17).

Performance of exercise results in acute physiologic responses and short- and long-term adaptations (6). Whether during a single training session (microcycle) or a block of training sessions (mesocycle), performance should be expected to increase or decrease in a predictable pattern based on the manipulation of acute programming variables. A deviation from this pattern may be indicative of an error in planning, such as too much or too little volume (13). However, variability is inherent in any individual (1), which may result in an unexpected increase or decrease in performance. Therefore, for time series data to be meaningful, removal of inherent variability is required.

Time series data consist of a systematic pattern and random noise (3). The systematic pattern is characterized by 2 components: (a) trend and (b) seasonality. The trend component involves a linear or nonlinear pattern that does not repeat over time. For example, the trend for an untrained individual's 1 repetition maximum (1RM) in a resistance exercise program is to increase in a nonlinear pattern, so long as the individual continues to train. The seasonality component involves a repeating pattern, such as described by a sine wave. For example, during an exercise program, an individual's 1RM may increase initially, followed by a plateau. An appropriate change to the exercise program will result in a further increase, followed by another plateau. This pattern is the basis for the periodization of resistance exercise programs (18). Conversely, random noise generates an unexpected and brief increase or decrease in the pattern, which may be the result of measurement error and/or variability as a result of physiologic and psychological factors.

Although time series analyses are routinely used across a diverse number of fields, (e.g., stock trading, real estate investment, and pharmacology research), to generate meaningful data for analysis and interpretation, its use in the assessment of athletic performance has not received much attention. Time series analyses require data smoothing to minimize the effects of random noise (3). A simple and commonly used method for data smoothing is the moving-average method, which averages a given number of data points surrounding the point of interest (3). The purpose of this report is to describe the use of time series analysis and the moving average technique to determine the systematic performance patterns within high-power resistance exercise bouts.


Experimental Approach to the Problem

Power athletes performed 3 high-power resistance exercise sessions. Each repetition was recorded using three-dimensional (3D) motion analysis to determine performance. The acute performance responses during each exercise session were determined by plotting performance during each set of exercises. To determine the systematic pattern, random noise was minimized using a moving average technique.


Men (n = 10) athletes competing in power sports (weightlifting, track and field, baseball) volunteered to participate. The participants were informed of the experimental risks and signed an informed consent document approved by the University of Southern California Health Sciences Institutional Review Board. All participants had 2 or more years of experience performing weight training exercises, including the clean or power clean. Participants were currently performing a strength and conditioning program for sports performance and data were collected in an off-season training phase.


Participants performed 3 exercise sessions approximately 1 week apart. The exercise sessions involved the clean pull performed at 75% 1RM for 5 repetitions per set for 12 sets, 85% 1RM/3 ×15 and 95%/1 × 20, with 3 minutes of rest between sets. Although atypical of athletic conditioning programs, the high number of sets was based on pilot research to determine the volume required to elicit a fatigue response. Loud verbal encouragement was provided during each exercise session.

An 8-camera optoelectronic motion analysis system (Vicon 612; Vicon, Los Angeles, California, USA) was used to record (fs = 120 Hz) reflective markers placed on participants and the center of the barbell. Markers on the participants were used to generate a lower-extremity link-segment model in Visual 3D software (version 3.13; C-Motion, Rockville, Maryland, USA). Vertical position coordinates from the barbell were analyzed in Datapac 2K2 software (version 3.14; Run Technologies, Mission Viejo, California, USA). Average barbell power was estimated as previously described (8). Briefly, work performed on the barbell was estimated from the change in potential (mg[Δh]) and kinetic (½m·[Δv]2) energies and divided by time. Velocity was calculated as the slope of linear regressions fitted at 5-ms intervals. The second pull was defined as the time from the end of the second knee bend (maximum knee flexion) to the time of peak vertical barbell velocity (12). The clean pull requires large mechanical work to be performed in a brief period of time, and average barbell power and peak barbell velocity are associated with success in weightlifting exercises (12). Coefficients of variation (CV) from a pilot study with 2 participants performing each protocol twice found peak potentiation (CV = 4.5-6.7%) and fatigue (CV = 4.1-8.6%) effects to be repeatable.

Statistical Analyses

For the multiple repetitions-per-set protocols, data were averaged across all repetitions in a set. Sets 2 and higher were fitted using a 3-point moving-average. For each protocol, the sets with the highest and lowest power output were determined. Changes in performance were analyzed using a 2 × 3 (raw vs. moving-average by first vs. highest vs. lowest set) repeated-measures analysis of variance (ANOVA). Where appropriate, Tukey post hoc tests were conducted.


Raw and moving-average data for each training session are presented in Figures 1 through 3. A significant interaction (p < 0.001) was observed for the 75% 1RM session. For the set with the highest power output, power was lower using the moving-average method (1,376 ± 216 W) compared to the raw data (1,403 ± 208 W; p = 0.006). For the set with the lowest power output, power was higher using the moving-average method (1,172 ± 252 W) compared to the raw data (1,118 ± 262W; p < 0.001). The increase in power for the highest set vs. first set was significant for both the raw and smoothed data (p < 0.001). The decrease in power for the lowest set vs. first set was significant for both the raw and smoothed data (p < 0.001).

Figure 1
Figure 1:
Average barbell power for 12 sets of 5 repetitions in the clean pull performed at 75% 1 repetition maximum (n = 10). Raw data-closed circles. Moving-average fitted data-open circles.

A significant interaction (p = 0.002) was observed for the 85% 1RM session. For the set with the highest power output, power was lower using the moving-average method (1,403 ± 239 W) compared to the raw data (1,451 ± 249 W; p = 0.009). For the set with the lowest power output, power was higher using the moving-average method (1,224 ± 312 W) compared to the raw data (1,174 ± 353 W; p = 0.007). The increase in power for the highest set vs. first set was significant for both the raw and smoothed data (p < 0.001). The decrease in power for the lowest set vs. first set was significant for the raw (p < 0.001) but not moving average (p = 0.13) data.

A significant interaction (p = 0.004) was also observed for the 95% 1RM session. For the set with the highest power output, power was not significantly different between the moving average (1,567 ± 352 W) and raw data (1,619 ± 409 W; p = 0.17). For the set with the lowest power output, power was higher using the moving-average method (1,265 ± 253 W) compared to the raw data (1,123 ± 282 W; p = 0.001). The increase in power for the highest set vs. first set was significant for both the raw and smoothed data (p < 0.006). The decrease in power for the lowest set vs. first set was significant for both the raw and smoothed data (p < 0.001).


In the 75% (Figure 1) and 85% (Figure 2) 1RM conditions, a systematic pattern was observed in the raw data; however, abrupt deviations to the pattern were also present. The moving-average method preserved the systematic pattern but removed the effects of these deviations. For example, in the 75% 1RM condition (Figure 1), a large decrease in performance occurred between set 8 and 9; however, performance increases between set 9 and 10. After using the moving average, the systematic pattern observed is consistent with the effects of postactivation potentiation and fatigue. In both protocols, the moving-average method attenuated the magnitudes of the postactivation potentiation and fatigue effects, which is a common feature of smoothing algorithms (3). In the 95% 1RM condition (Figure 3), no systematic pattern could be detected in the raw data because of the amount of noise present. The moving-average method reduced the random noise, allowing the systematic pattern to be observed. It is interesting that, although the magnitude of the fatigue effects was attenuated in this protocol, the magnitude of the postactivation potentiation was not.

Figure 2
Figure 2:
Average barbell power for 15 sets of 3 repetitions in the clean pull performed at 85% 1 repetition maximum (n = 10). Raw data-closed circles. Moving-average fitted data-open circles.
Figure 3
Figure 3:
Average barbell power for 20 sets of 1 repetition performed at 95% 1 repetition maximum protocol (n = 10). Raw data-closed circles. Moving-average fitted data-open circles.

In measurement and testing, random noise refers to measurement error. However, when evaluating human performance over time, random noise may also be a result of psychological factors or inherent variability in the neuromuscular system. A common concern during strength training and research investigations is eliciting appropriate effort from participants. Previous investigations have demonstrated that individuals participating in supervised resistance exercise programs elicit greater adaptations than unsupervised individuals (10,16). This effect has been demonstrated in both sedentary individuals and trained athletes. For the current investigation, loud verbal encouragement was provided to participants during each exercise session as an external source of motivation.

Potential sources of variability within the neuromuscular system can be found in both the peripheral and central nervous systems. In the peripheral nervous system, 2 types of fatigue have been demonstrated during high-intensity tasks such as resistance exercise. Fatigue observed following multiple sets of exercise appears to be from an intramuscular accumulation of calcium ions resulting from a decrease in calcium ion pump activity (20). Fatigue may also manifest immediately following a single set of exercise through intermuscular mechanisms (5). Following high force muscle contractions, the sodium and potassium ion balance across the muscle sarcolemma and motor nerves needs to be restored before further force generation. The time required to recover from intermuscular fatigue is brief (1-4 minutes), depending on the volume of exercise performed in the set. During high-load resistance training, for successive 1RM attempts, only 1 minute is required for recovery (15), whereas for 5RM (approximately 80-85% 1RM) sets, 2 to 5 minutes is required for recovery (21). However, it is not known whether these same rest intervals apply for high-power resistance exercise. Additionally, when a high number of sets are performed, it is possible that the cumulative stress imposed on the sarcolemma and motor nerves alters the time required to restore the sodium and potassium ion balance (5). Thus, variability in the rate of recovery from intermuscular fatigue is a plausible mechanism for the noise observed during the exercise sessions.

In the central nervous system, skilled motor tasks, such as the clean pull, are controlled by the motor cortex, utilizing feedback from sensory receptors and the cerebellum to correct movements. Although skilled performers are able to generate the same task outcome during repetitive trials, the movement patterns utilized to reach this outcome are often variable (1,11). For example, the fundamental task outcome of the clean pull is to impart momentum to the barbell at the end of the second pull (12). To reach this task outcome, athletes lift the barbell from the floor in a stoop posture (first pull), reposition their body to an upright posture (second knee bend), and rapidly extend at the hip and knee joints (second pull). As a result of these 3 phases and the numerous muscles and joints involved, the degrees of freedom and thus potential variability are high. Thus, it is also likely that interjoint variability during motor task execution may contribute to the noise observed during high-power exercise. The significance of variability during execution of motor tasks is unclear, and little research has been published specifically examining performance variability during weightlifting.

For the purpose of examining acute performance responses during resistance exercise, the moving-average method of processing time series data appears to be appropriate, allowing systematic patterns to be determined. This method may also be useful in analyzing performance across multiple days, weeks, or months. Measurement of changes in strength and power are often recommended over the course of a macrocycle. Research in periodization suggests that more frequent measurements may be useful to determine (a) if the training stimulus is sufficient to elicit adaptations and (b) to determine if the athlete is at risk of overtraining (17). However, the effects of inherent variability will be greater with an increase in the frequency of measurements, obscuring the systematic pattern. Sudden increases or decreases in performance may be accounted for by physiologic factors including sleep deprivation (2), stimulant use (19), and psychological factors. Theoretically, time series analysis techniques may reduce the effects of these factors, allowing coaches to make meaningful inferences regarding the effectiveness of a training program. Further research is required to determine the value of time series analysis for studying interday performance across short- and long-term training protocols.

Practical Applications

The moving-average technique was applied to reduce the effect of noise on acute performance responses during high-power resistance exercise, allowing a systematic pattern, consistent with postactivation potentiation and fatigue effects, to be determined. With technological advances in sport science and their increasing availability to coaches and researchers, frequent performance measurements can be taken. Practitioners should be aware of variability during exercise performance, which may result in unexpected increases or decreases in performance. Variability suggests that abrupt changes in performance may not be a cause for alarm and should be considered in context with the systematic pattern. Within an exercise session, utilizing the moving average technique to analyze time series data allows coaches to determine when performance is increasing and decreasing. Consistent decreases in performance may warrant reducing the training intensity or terminating the exercise session. The moving average technique may also be applicable for analyzing short- and long-term changes in performance, which are subject to variance as a result of physiologic and psychological factors.


1. Bernstein, N. The Co-ordination and Regulation of Movements. Oxford, England: Pergamon Press, 1967.
2. Blumert, PA, Crum, AJ, Ernsting, M, Volek, JS, Hollander, DB, Haff, EE, and Haff, GG. The acute effects of twenty-four hours of sleep loss on the performance of national-caliber male collegiate weightlifters. J Strength Cond Res 21: 1146-1154, 2007.
3. Box, GEP and Jenkins, GM. Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day, 1976.
4. Bruenger, AJ, Smith, SL, Sands, WA, and Leigh, MR. Validation of instrumentation to monitor dynamic performance of Olympic weightlifters. J Strength Cond Res 21: 492-499, 2007.
5. Cheng, AJ and Rice, CL. Fatigue and recovery of power and isometric torque following isotonic knee extensions. J Appl Physiol 99: 1446-1452, 2005.
6. Chiu, LZF and Barnes, JL. The fitness-fatigue model revisited: Implications for planning short- and long-term training. Strength Cond J 25: 42-51, 2003.
7. Chiu, LZF, Fry, AC, Schilling, BK, Johnson, EJ, and Weiss, LW. Neuromuscular fatigue and potentiation following two successive high intensity resistance exercise sessions. Eur J Appl Physiol 92: 385-392, 2004.
8. Chiu, LZF, Schilling, BK, Fry, AC, and Salem, GJ. The influence of deformation on barbell mechanics during the clean pull. Sports Biomech 7: 260-273, 2008.
9. Chiu, LZF, Fry, AC, Schilling, BK, Fry, AC, and Weiss, LW. Measurement of resistance exercise force expression. J Appl Biomech 20: 204-212, 2004.
10. Coutts, AJ, Murphy, AJ, and Dascombe, BJ. Effect of direct supervision of a strength coach on measures of muscular strength and power in young rugby league players. J Strength Cond Res 18: 316-323, 2004.
11. Davids, K, Glazier, P, Araújo, D, and Bartlett, R. Movement systems as dynamical systems. The functional role of variability and its implications for sports medicine. Sports Med 33: 245-260, 2003.
12. Garhammer, J. A review of power output studies of Olympic and powerlifting: Methodology, performance prediction, and evaluation tests. J Strength Cond Res 7: 76-89, 1993.
13. González-Badillo, JJ, Izquierdo, M, and Gorostiaga, EM. Moderate volume of high relative training intensity produces greater strength gains compared with low and high volumes in competitive weightlifters. J Strength Cond Res 20: 73-81, 2006.
14. Lim, JM and Chia, MYH. Reliability of power output derived from the nonmotorized treadmill test. J Strength Cond Res 21: 993-996, 2007.
15. Matuszak, ME, Fry, AC, Weiss, LW, Ireland, TR, and McKnight, MM. Effect of rest interval length on repeated 1 repetition maximum back squats. J Strength Cond Res 17: 634-637, 2003.
16. Mazzetti, SA, Kraemer, WJ, Volek, JS, Duncan, ND, Ratamess, RA, Gomez, AL, Newton, RU, Häkkinen, K, and Fleck, SJ. The influence of direct supervision of resistance training on strength performance. Med Sci Sports Exerc 32: 1175-1184, 2000.
17. Moore, CA and Fry, AC. Nonfunctional overreaching during off-season training for skill position players in collegiate American football. J Strength Cond Res 21: 793-800, 2007.
18. Plisk, SS and Stone, MH. Periodization strategies. Strength Cond J 25: 19-37, 2003.
19. Spriet, LL and Gibala, MJ. Nutritional strategies to influence adaptations to training. J Sports Sci 22: 127-141, 2004.
20. Tupling, R, Green, H, Grant, S, Burnett, M, and Ranney, D. Postcontractile force depression in humans is associated with an impairment in SR Ca2+ pump function. Am J Physiol 278: R87-R94, 2000.
21. Willardson, JM and Burkett, LN. A comparison of 3 different rest intervals on the exercise volume completed during a workout. J Strength Cond Res 19: 23-26, 2005.

performance evaluation; acute physiologic responses; postactivation potentiation; fatigue

© 2010 National Strength and Conditioning Association