Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 30.88% per annum.
- CRM price at the close of December 17, 2025 was $258.14 and was higher than the top border of the primary price channel by $6.39 (2.54%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 15.65% per annum.
- CRM price at the close of December 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 CRM 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: November 7, 2024
End date: December 3, 2025
a = 7.2583
b = -0.0010
s = 0.0585
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0010) – 1
= -30.88%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0585) – 1
= 26.37%
November 7, 2024 calculations
Top border of price channel:
Exp(Y977)
= Exp(a + b × X977 + 2 × s)
= Exp(a + b × 1,420 + 2 × s)
= Exp(7.2583 + -0.0010 × 1,420 + 2 × 0.0585)
= Exp(5.9383)
= $379.29
Bottom border of price channel:
Exp(Y977)
= Exp(a + b × X977 – 2 × s)
= Exp(a + b × 1,420 – 2 × s)
= Exp(7.2583 + -0.0010 × 1,420 – 2 × 0.0585)
= Exp(5.7043)
= $300.15
December 3, 2025 calculations
Top border of price channel:
Exp(Y1,244)
= Exp(a + b × X1,244 + 2 × s)
= Exp(a + b × 1,811 + 2 × s)
= Exp(7.2583 + -0.0010 × 1,811 + 2 × 0.0585)
= Exp(5.5426)
= $255.34
Bottom border of price channel:
Exp(Y1,244)
= Exp(a + b × X1,244 – 2 × s)
= Exp(a + b × 1,811 – 2 × s)
= Exp(7.2583 + -0.0010 × 1,811 – 2 × 0.0585)
= Exp(5.3086)
= $202.06
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 30.88% per annum.
- CRM price at the close of December 17, 2025 was $258.14 and was higher than the top border of the primary price channel by $6.39 (2.54%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: March 6, 2025
End date: December 17, 2025
a = 6.3321
b = -0.0005
s = 0.0455
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0005) – 1
= -15.65%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0455) – 1
= 19.95%
March 6, 2025 calculations
Top border of price channel:
Exp(Y1,056)
= Exp(a + b × X1,056 + 2 × s)
= Exp(a + b × 1,539 + 2 × s)
= Exp(6.3321 + -0.0005 × 1,539 + 2 × 0.0455)
= Exp(5.7057)
= $300.57
Bottom border of price channel:
Exp(Y1,056)
= Exp(a + b × X1,056 – 2 × s)
= Exp(a + b × 1,539 – 2 × s)
= Exp(6.3321 + -0.0005 × 1,539 – 2 × 0.0455)
= Exp(5.5238)
= $250.58
December 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(6.3321 + -0.0005 × 1,825 + 2 × 0.0455)
= Exp(5.5724)
= $263.05
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(6.3321 + -0.0005 × 1,825 – 2 × 0.0455)
= Exp(5.3904)
= $219.30
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 15.65% per annum.
- CRM price at the close of December 17, 2025 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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