Paychex Inc (PAYX)
Paychex, Inc. is an American provider of human resource, payroll, and benefits outsourcing services for small- to medium-sized businesses.
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 38.61% per annum.
- PAYX price at the close of September 17, 2025 was $132.46 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 56.56% per annum.
- PAYX price at the close of September 17, 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 15, 2025
End date: September 17, 2025
a = 7.3299
b = -0.0013
s = 0.0202
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0013) – 1
= -38.61%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0202) – 1
= 8.43%
May 15, 2025 calculations
Top border of price channel:
Exp(Y1,169)
= Exp(a + b × X1,169 + 2 × s)
= Exp(a + b × 1,700 + 2 × s)
= Exp(7.3299 + -0.0013 × 1,700 + 2 × 0.0202)
= Exp(5.0979)
= $163.68
Bottom border of price channel:
Exp(Y1,169)
= Exp(a + b × X1,169 – 2 × s)
= Exp(a + b × 1,700 – 2 × s)
= Exp(7.3299 + -0.0013 × 1,700 – 2 × 0.0202)
= Exp(5.0170)
= $150.95
September 17, 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(7.3299 + -0.0013 × 1,825 + 2 × 0.0202)
= Exp(4.9308)
= $138.49
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(7.3299 + -0.0013 × 1,825 – 2 × 0.0202)
= Exp(4.8499)
= $127.72
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 38.61% per annum.
- PAYX price at the close of September 17, 2025 was $132.46 and was inside the primary price channel.
Secondary Trend
Start date: August 22, 2025
End date: September 17, 2025
a = 9.0537
b = -0.0023
s = 0.0070
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0023) – 1
= -56.56%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0070) – 1
= 2.83%
August 22, 2025 calculations
Top border of price channel:
Exp(Y1,237)
= Exp(a + b × X1,237 + 2 × s)
= Exp(a + b × 1,799 + 2 × s)
= Exp(9.0537 + -0.0023 × 1,799 + 2 × 0.0070)
= Exp(4.9575)
= $142.24
Bottom border of price channel:
Exp(Y1,237)
= Exp(a + b × X1,237 – 2 × s)
= Exp(a + b × 1,799 – 2 × s)
= Exp(9.0537 + -0.0023 × 1,799 – 2 × 0.0070)
= Exp(4.9296)
= $138.33
September 17, 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(9.0537 + -0.0023 × 1,825 + 2 × 0.0070)
= Exp(4.8981)
= $134.04
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(9.0537 + -0.0023 × 1,825 – 2 × 0.0070)
= Exp(4.8702)
= $130.35
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 56.56% per annum.
- PAYX price at the close of September 17, 2025 was inside the secondary price channel.