Paychex Inc (PAYX)
Paychex, Inc. is a leading provider of comprehensive human resource, payroll, and benefits outsourcing solutions tailored specifically for small- and medium-sized businesses. Headquartered in Rochester, New York, the company leverages advanced technology and a client-centric approach to streamline workforce management processes for its clients. Committed to delivering value and efficiency, Paychex offers a robust suite of services, including payroll processing, tax administration, and employee benefit management. With a strong reputation for reliability and customer service, Paychex continues to expand its footprint in the HR services market, making it a key player in supporting the growth and success of its clients.
Stock Price Trends
Stock price trends estimated using linear regression.
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 44.43% per annum.
- PAYX price at the close of January 8, 2026 was $114.25 and was higher than the top border of the primary price channel by $0.51 (0.45%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.99% per annum.
- PAYX price at the close of January 8, 2026 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of PAYX price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: May 15, 2025
End date: January 7, 2026
a = 7.6118
b = -0.0016
s = 0.0283
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0016) – 1
= -44.43%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0283) – 1
= 11.98%
May 15, 2025 calculations
Top border of price channel:
Exp(Y1,091)
= Exp(a + b × X1,091 + 2 × s)
= Exp(a + b × 1,585 + 2 × s)
= Exp(7.6118 + -0.0016 × 1,585 + 2 × 0.0283)
= Exp(5.1170)
= $166.84
Bottom border of price channel:
Exp(Y1,091)
= Exp(a + b × X1,091 – 2 × s)
= Exp(a + b × 1,585 – 2 × s)
= Exp(7.6118 + -0.0016 × 1,585 – 2 × 0.0283)
= Exp(5.0039)
= $148.99
January 7, 2026 calculations
Top border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 + 2 × s)
= Exp(a + b × 1,822 + 2 × s)
= Exp(7.6118 + -0.0016 × 1,822 + 2 × 0.0283)
= Exp(4.7355)
= $113.92
Bottom border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 – 2 × s)
= Exp(a + b × 1,822 – 2 × s)
= Exp(7.6118 + -0.0016 × 1,822 – 2 × 0.0283)
= Exp(4.6224)
= $101.73
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 44.43% per annum.
- PAYX price at the close of January 8, 2026 was $114.25 and was higher than the top border of the primary price channel by $0.51 (0.45%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: November 6, 2025
End date: January 8, 2026
a = 4.1217
b = 0.0003
s = 0.0161
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 12.99%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0161) – 1
= 6.66%
November 6, 2025 calculations
Top border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 + 2 × s)
= Exp(a + b × 1,760 + 2 × s)
= Exp(4.1217 + 0.0003 × 1,760 + 2 × 0.0161)
= Exp(4.7430)
= $114.78
Bottom border of price channel:
Exp(Y1,212)
= Exp(a + b × X1,212 – 2 × s)
= Exp(a + b × 1,760 – 2 × s)
= Exp(4.1217 + 0.0003 × 1,760 – 2 × 0.0161)
= Exp(4.6785)
= $107.61
January 8, 2026 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(4.1217 + 0.0003 × 1,823 + 2 × 0.0161)
= Exp(4.7641)
= $117.23
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.1217 + 0.0003 × 1,823 – 2 × 0.0161)
= Exp(4.6996)
= $109.91
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.99% per annum.
- PAYX price at the close of January 8, 2026 was inside the secondary price channel.