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 46.99% per annum.
- PAYX price at the close of November 24, 2025 was $109.91 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 78.54% per annum.
- PAYX price at the close of November 24, 2025 was inside the secondary price channel.
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 16, 2025
End date: November 24, 2025
a = 7.9085
b = -0.0017
s = 0.0271
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0017) – 1
= -46.99%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0271) – 1
= 11.43%
May 16, 2025 calculations
Top border of price channel:
Exp(Y1,122)
= Exp(a + b × X1,122 + 2 × s)
= Exp(a + b × 1,633 + 2 × s)
= Exp(7.9085 + -0.0017 × 1,633 + 2 × 0.0271)
= Exp(5.1231)
= $167.86
Bottom border of price channel:
Exp(Y1,122)
= Exp(a + b × X1,122 – 2 × s)
= Exp(a + b × 1,633 – 2 × s)
= Exp(7.9085 + -0.0017 × 1,633 – 2 × 0.0271)
= Exp(5.0149)
= $150.64
November 24, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(7.9085 + -0.0017 × 1,825 + 2 × 0.0271)
= Exp(4.7893)
= $120.21
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(7.9085 + -0.0017 × 1,825 – 2 × 0.0271)
= Exp(4.6811)
= $107.89
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 46.99% per annum.
- PAYX price at the close of November 24, 2025 was $109.91 and was inside the primary price channel.
Secondary Trend
Start date: October 13, 2025
End date: November 24, 2025
a = 12.3649
b = -0.0042
s = 0.0181
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0042) – 1
= -78.54%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0181) – 1
= 7.49%
October 13, 2025 calculations
Top border of price channel:
Exp(Y1,224)
= Exp(a + b × X1,224 + 2 × s)
= Exp(a + b × 1,783 + 2 × s)
= Exp(12.3649 + -0.0042 × 1,783 + 2 × 0.0181)
= Exp(4.8841)
= $132.17
Bottom border of price channel:
Exp(Y1,224)
= Exp(a + b × X1,224 – 2 × s)
= Exp(a + b × 1,783 – 2 × s)
= Exp(12.3649 + -0.0042 × 1,783 – 2 × 0.0181)
= Exp(4.8119)
= $122.96
November 24, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(12.3649 + -0.0042 × 1,825 + 2 × 0.0181)
= Exp(4.7070)
= $110.72
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(12.3649 + -0.0042 × 1,825 – 2 × 0.0181)
= Exp(4.6348)
= $103.01
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 78.54% per annum.
- PAYX price at the close of November 24, 2025 was inside the secondary price channel.